diff --git a/src/testdir/dumps/Test_set_tagfunc_on_cmdline.dump b/src/testdir/dumps/Test_set_tagfunc_on_cmdline.dump
deleted file mode 100644
index b81d99c..0000000
--- a/src/testdir/dumps/Test_set_tagfunc_on_cmdline.dump
+++ /dev/null
@@ -1,6 +0,0 @@
-| +0&#ffffff0@74
-@75
-@75
-|E+0#ffffff16#e000002|r@1|o|r| |d|e|t|e|c|t|e|d| |w|h|i|l|e| |p|r|o|c|e|s@1|i|n|g| |c|o|m@1|a|n|d| |l|i|n|e|:| +0#0000000#ffffff0@29
-|E+0#ffffff16#e000002|4|7|4|:| |I|n|v|a|l|i|d| |a|r|g|u|m|e|n|t|:| |t|a|g|f|u|n|c|=|s|:|F|u|n|c| +0#0000000#ffffff0@36
-|P+0#00e0003&|r|e|s@1| |E|N|T|E|R| |o|r| |t|y|p|e| |c|o|m@1|a|n|d| |t|o| |c|o|n|t|i|n|u|e> +0#0000000&@35
diff --git a/src/testdir/test_ins_complete.vim b/src/testdir/test_ins_complete.vim
index d2e2c11..e3d23e7 100644
--- a/src/testdir/test_ins_complete.vim
+++ b/src/testdir/test_ins_complete.vim
@@ -880,13 +880,13 @@
   endfunc
 
   let lines =<< trim END
-    #" Test for using a function name
+    #" Test for using a global function name
     LET &completefunc = 'g:CompleteFunc2'
     new
-    call setline(1, 'zero')
+    call setline(1, 'global')
     LET g:CompleteFunc2Args = []
     call feedkeys("A\<C-X>\<C-U>\<Esc>", 'x')
-    call assert_equal([[1, ''], [0, 'zero']], g:CompleteFunc2Args)
+    call assert_equal([[1, ''], [0, 'global']], g:CompleteFunc2Args)
     bw!
 
     #" Test for using a function()
@@ -1022,6 +1022,29 @@
   END
   call CheckLegacyAndVim9Success(lines)
 
+  " Test for using a script-local function name
+  func s:CompleteFunc3(findstart, base)
+    call add(g:CompleteFunc3Args, [a:findstart, a:base])
+    return a:findstart ? 0 : []
+  endfunc
+  set completefunc=s:CompleteFunc3
+  new
+  call setline(1, 'script1')
+  let g:CompleteFunc3Args = []
+  call feedkeys("A\<C-X>\<C-U>\<Esc>", 'x')
+  call assert_equal([[1, ''], [0, 'script1']], g:CompleteFunc3Args)
+  bw!
+
+  let &completefunc = 's:CompleteFunc3'
+  new
+  call setline(1, 'script2')
+  let g:CompleteFunc3Args = []
+  call feedkeys("A\<C-X>\<C-U>\<Esc>", 'x')
+  call assert_equal([[1, ''], [0, 'script2']], g:CompleteFunc3Args)
+  bw!
+  delfunc s:CompleteFunc3
+
+  " invalid return value
   let &completefunc = {a -> 'abc'}
   call feedkeys("A\<C-X>\<C-U>\<Esc>", 'x')
 
@@ -1056,11 +1079,12 @@
   let lines =<< trim END
     vim9script
 
-    # Test for using a def function with completefunc
-    def Vim9CompleteFunc(val: number, findstart: number, base: string): any
-      add(g:Vim9completeFuncArgs, [val, findstart, base])
+    def Vim9CompleteFunc(callnr: number, findstart: number, base: string): any
+      add(g:Vim9completeFuncArgs, [callnr, findstart, base])
       return findstart ? 0 : []
     enddef
+
+    # Test for using a def function with completefunc
     set completefunc=function('Vim9CompleteFunc',\ [60])
     new | only
     setline(1, 'one')
@@ -1068,6 +1092,28 @@
     feedkeys("A\<C-X>\<C-U>\<Esc>", 'x')
     assert_equal([[60, 1, ''], [60, 0, 'one']], g:Vim9completeFuncArgs)
     bw!
+
+    # Test for using a global function name
+    &completefunc = g:CompleteFunc2
+    new | only
+    setline(1, 'two')
+    g:CompleteFunc2Args = []
+    feedkeys("A\<C-X>\<C-U>\<Esc>", 'x')
+    assert_equal([[1, ''], [0, 'two']], g:CompleteFunc2Args)
+    bw!
+
+    # Test for using a script-local function name
+    def s:LocalCompleteFunc(findstart: number, base: string): any
+      add(g:LocalCompleteFuncArgs, [findstart, base])
+      return findstart ? 0 : []
+    enddef
+    &completefunc = s:LocalCompleteFunc
+    new | only
+    setline(1, 'three')
+    g:LocalCompleteFuncArgs = []
+    feedkeys("A\<C-X>\<C-U>\<Esc>", 'x')
+    assert_equal([[1, ''], [0, 'three']], g:LocalCompleteFuncArgs)
+    bw!
   END
   call CheckScriptSuccess(lines)
 
@@ -1233,6 +1279,29 @@
   END
   call CheckLegacyAndVim9Success(lines)
 
+  " Test for using a script-local function name
+  func s:OmniFunc3(findstart, base)
+    call add(g:OmniFunc3Args, [a:findstart, a:base])
+    return a:findstart ? 0 : []
+  endfunc
+  set omnifunc=s:OmniFunc3
+  new
+  call setline(1, 'script1')
+  let g:OmniFunc3Args = []
+  call feedkeys("A\<C-X>\<C-O>\<Esc>", 'x')
+  call assert_equal([[1, ''], [0, 'script1']], g:OmniFunc3Args)
+  bw!
+
+  let &omnifunc = 's:OmniFunc3'
+  new
+  call setline(1, 'script2')
+  let g:OmniFunc3Args = []
+  call feedkeys("A\<C-X>\<C-O>\<Esc>", 'x')
+  call assert_equal([[1, ''], [0, 'script2']], g:OmniFunc3Args)
+  bw!
+  delfunc s:OmniFunc3
+
+  " invalid return value
   let &omnifunc = {a -> 'abc'}
   call feedkeys("A\<C-X>\<C-O>\<Esc>", 'x')
 
@@ -1267,11 +1336,12 @@
   let lines =<< trim END
     vim9script
 
-    # Test for using a def function with omnifunc
-    def Vim9omniFunc(val: number, findstart: number, base: string): any
-      add(g:Vim9omniFunc_Args, [val, findstart, base])
+    def Vim9omniFunc(callnr: number, findstart: number, base: string): any
+      add(g:Vim9omniFunc_Args, [callnr, findstart, base])
       return findstart ? 0 : []
     enddef
+
+    # Test for using a def function with omnifunc
     set omnifunc=function('Vim9omniFunc',\ [60])
     new | only
     setline(1, 'one')
@@ -1279,6 +1349,28 @@
     feedkeys("A\<C-X>\<C-O>\<Esc>", 'x')
     assert_equal([[60, 1, ''], [60, 0, 'one']], g:Vim9omniFunc_Args)
     bw!
+
+    # Test for using a global function name
+    &omnifunc = g:OmniFunc2
+    new | only
+    setline(1, 'two')
+    g:OmniFunc2Args = []
+    feedkeys("A\<C-X>\<C-O>\<Esc>", 'x')
+    assert_equal([[1, ''], [0, 'two']], g:OmniFunc2Args)
+    bw!
+
+    # Test for using a script-local function name
+    def s:LocalOmniFunc(findstart: number, base: string): any
+      add(g:LocalOmniFuncArgs, [findstart, base])
+      return findstart ? 0 : []
+    enddef
+    &omnifunc = s:LocalOmniFunc
+    new | only
+    setline(1, 'three')
+    g:LocalOmniFuncArgs = []
+    feedkeys("A\<C-X>\<C-O>\<Esc>", 'x')
+    assert_equal([[1, ''], [0, 'three']], g:LocalOmniFuncArgs)
+    bw!
   END
   call CheckScriptSuccess(lines)
 
@@ -1467,6 +1559,29 @@
   END
   call CheckLegacyAndVim9Success(lines)
 
+  " Test for using a script-local function name
+  func s:TsrFunc3(findstart, base)
+    call add(g:TsrFunc3Args, [a:findstart, a:base])
+    return a:findstart ? 0 : []
+  endfunc
+  set tsrfu=s:TsrFunc3
+  new
+  call setline(1, 'script1')
+  let g:TsrFunc3Args = []
+  call feedkeys("A\<C-X>\<C-T>\<Esc>", 'x')
+  call assert_equal([[1, ''], [0, 'script1']], g:TsrFunc3Args)
+  bw!
+
+  let &tsrfu = 's:TsrFunc3'
+  new
+  call setline(1, 'script2')
+  let g:TsrFunc3Args = []
+  call feedkeys("A\<C-X>\<C-T>\<Esc>", 'x')
+  call assert_equal([[1, ''], [0, 'script2']], g:TsrFunc3Args)
+  bw!
+  delfunc s:TsrFunc3
+
+  " invalid return value
   let &thesaurusfunc = {a -> 'abc'}
   call feedkeys("A\<C-X>\<C-T>\<Esc>", 'x')
 
@@ -1514,11 +1629,12 @@
   let lines =<< trim END
     vim9script
 
-    # Test for using a def function with thesaurusfunc
-    def Vim9tsrFunc(val: number, findstart: number, base: string): any
-      add(g:Vim9tsrFunc_Args, [val, findstart, base])
+    def Vim9tsrFunc(callnr: number, findstart: number, base: string): any
+      add(g:Vim9tsrFunc_Args, [callnr, findstart, base])
       return findstart ? 0 : []
     enddef
+
+    # Test for using a def function with thesaurusfunc
     set thesaurusfunc=function('Vim9tsrFunc',\ [60])
     new | only
     setline(1, 'one')
@@ -1526,6 +1642,28 @@
     feedkeys("A\<C-X>\<C-T>\<Esc>", 'x')
     assert_equal([[60, 1, ''], [60, 0, 'one']], g:Vim9tsrFunc_Args)
     bw!
+
+    # Test for using a global function name
+    &thesaurusfunc = g:TsrFunc2
+    new | only
+    setline(1, 'two')
+    g:TsrFunc2Args = []
+    feedkeys("A\<C-X>\<C-T>\<Esc>", 'x')
+    assert_equal([[1, ''], [0, 'two']], g:TsrFunc2Args)
+    bw!
+
+    # Test for using a script-local function name
+    def s:LocalTsrFunc(findstart: number, base: string): any
+      add(g:LocalTsrFuncArgs, [findstart, base])
+      return findstart ? 0 : []
+    enddef
+    &thesaurusfunc = s:LocalTsrFunc
+    new | only
+    setline(1, 'three')
+    g:LocalTsrFuncArgs = []
+    feedkeys("A\<C-X>\<C-T>\<Esc>", 'x')
+    assert_equal([[1, ''], [0, 'three']], g:LocalTsrFuncArgs)
+    bw!
   END
   call CheckScriptSuccess(lines)
 
diff --git a/src/testdir/test_normal.vim b/src/testdir/test_normal.vim
index 2f9b1ce..08539de 100644
--- a/src/testdir/test_normal.vim
+++ b/src/testdir/test_normal.vim
@@ -575,6 +575,21 @@
   END
   call CheckTransLegacySuccess(lines)
 
+  " Test for using a script-local function name
+  func s:OpFunc3(type)
+    let g:OpFunc3Args = [a:type]
+  endfunc
+  set opfunc=s:OpFunc3
+  let g:OpFunc3Args = []
+  normal! g@l
+  call assert_equal(['char'], g:OpFunc3Args)
+
+  let &opfunc = 's:OpFunc3'
+  let g:OpFunc3Args = []
+  normal! g@l
+  call assert_equal(['char'], g:OpFunc3Args)
+  delfunc s:OpFunc3
+
   " Using Vim9 lambda expression in legacy context should fail
   set opfunc=(a)\ =>\ OpFunc1(24,\ a)
   let g:OpFunc1Args = []
@@ -598,14 +613,32 @@
   let lines =<< trim END
     vim9script
 
-    # Test for using a def function with opfunc
     def g:Vim9opFunc(val: number, type: string): void
       g:OpFunc1Args = [val, type]
     enddef
+
+    # Test for using a def function with opfunc
     set opfunc=function('g:Vim9opFunc',\ [60])
     g:OpFunc1Args = []
     normal! g@l
     assert_equal([60, 'char'], g:OpFunc1Args)
+
+    # Test for using a global function name
+    &opfunc = g:OpFunc2
+    g:OpFunc2Args = []
+    normal! g@l
+    assert_equal(['char'], g:OpFunc2Args)
+    bw!
+
+    # Test for using a script-local function name
+    def s:LocalOpFunc(type: string): void
+      g:LocalOpFuncArgs = [type]
+    enddef
+    &opfunc = s:LocalOpFunc
+    g:LocalOpFuncArgs = []
+    normal! g@l
+    assert_equal(['char'], g:LocalOpFuncArgs)
+    bw!
   END
   call CheckScriptSuccess(lines)
 
diff --git a/src/testdir/test_quickfix.vim b/src/testdir/test_quickfix.vim
index 895c52a..511896e 100644
--- a/src/testdir/test_quickfix.vim
+++ b/src/testdir/test_quickfix.vim
@@ -5387,6 +5387,23 @@
   END
   call CheckLegacyAndVim9Success(lines)
 
+  " Test for using a script-local function name
+  func s:TqfFunc2(info)
+    let g:TqfFunc2Args = [a:info.start_idx, a:info.end_idx]
+    return ''
+  endfunc
+  let g:TqfFunc2Args = []
+  set quickfixtextfunc=s:TqfFunc2
+  cexpr "F10:10:10:L10"
+  cclose
+  call assert_equal([1, 1], g:TqfFunc2Args)
+
+  let &quickfixtextfunc = 's:TqfFunc2'
+  cexpr "F11:11:11:L11"
+  cclose
+  call assert_equal([1, 1], g:TqfFunc2Args)
+  delfunc s:TqfFunc2
+
   " set 'quickfixtextfunc' to a partial with dict. This used to cause a crash.
   func SetQftfFunc()
     let params = {'qftf': function('g:DictQftfFunc')}
diff --git a/src/testdir/test_tagfunc.vim b/src/testdir/test_tagfunc.vim
index d07aa07..03394ac 100644
--- a/src/testdir/test_tagfunc.vim
+++ b/src/testdir/test_tagfunc.vim
@@ -267,38 +267,62 @@
   END
   call CheckLegacyAndVim9Success(lines)
 
+  " Test for using a script-local function name
+  func s:TagFunc3(pat, flags, info)
+    let g:TagFunc3Args = [a:pat, a:flags, a:info]
+    return v:null
+  endfunc
+  set tagfunc=s:TagFunc3
+  new
+  let g:TagFunc3Args = []
+  call assert_fails('tag a21', 'E433:')
+  call assert_equal(['a21', '', {}], g:TagFunc3Args)
+  bw!
+  let &tagfunc = 's:TagFunc3'
+  new
+  let g:TagFunc3Args = []
+  call assert_fails('tag a22', 'E433:')
+  call assert_equal(['a22', '', {}], g:TagFunc3Args)
+  bw!
+  delfunc s:TagFunc3
+
+  " invalid return value
   let &tagfunc = "{a -> 'abc'}"
   call assert_fails("echo taglist('a')", "E987:")
 
   " Using Vim9 lambda expression in legacy context should fail
   set tagfunc=(a,\ b,\ c)\ =>\ g:TagFunc1(21,\ a,\ b,\ c)
-  new | only
+  new
   let g:TagFunc1Args = []
   call assert_fails("tag a17", "E117:")
   call assert_equal([], g:TagFunc1Args)
+  bw!
 
   " Test for using a script local function
   set tagfunc=<SID>ScriptLocalTagFunc
-  new | only
+  new
   let g:ScriptLocalFuncArgs = []
   call assert_fails('tag a15', 'E433:')
   call assert_equal(['a15', '', {}], g:ScriptLocalFuncArgs)
+  bw!
 
   " Test for using a script local funcref variable
   let Fn = function("s:ScriptLocalTagFunc")
   let &tagfunc= Fn
-  new | only
+  new
   let g:ScriptLocalFuncArgs = []
   call assert_fails('tag a16', 'E433:')
   call assert_equal(['a16', '', {}], g:ScriptLocalFuncArgs)
+  bw!
 
   " Test for using a string(script local funcref variable)
   let Fn = function("s:ScriptLocalTagFunc")
   let &tagfunc= string(Fn)
-  new | only
+  new
   let g:ScriptLocalFuncArgs = []
   call assert_fails('tag a16', 'E433:')
   call assert_equal(['a16', '', {}], g:ScriptLocalFuncArgs)
+  bw!
 
   " set 'tagfunc' to a partial with dict. This used to cause a crash.
   func SetTagFunc()
@@ -324,16 +348,37 @@
   let lines =<< trim END
     vim9script
 
-    # Test for using function()
-    def Vim9tagFunc(val: number, pat: string, flags: string, info: dict<any>): any
-      g:Vim9tagFuncArgs = [val, pat, flags, info]
+    def Vim9tagFunc(callnr: number, pat: string, flags: string, info: dict<any>): any
+      g:Vim9tagFuncArgs = [callnr, pat, flags, info]
       return null
     enddef
+
+    # Test for using a def function with completefunc
     set tagfunc=function('Vim9tagFunc',\ [60])
-    new | only
+    new
     g:Vim9tagFuncArgs = []
     assert_fails('tag a10', 'E433:')
     assert_equal([60, 'a10', '', {}], g:Vim9tagFuncArgs)
+
+    # Test for using a global function name
+    &tagfunc = g:TagFunc2
+    new
+    g:TagFunc2Args = []
+    assert_fails('tag a11', 'E433:')
+    assert_equal(['a11', '', {}], g:TagFunc2Args)
+    bw!
+
+    # Test for using a script-local function name
+    def s:LocalTagFunc(pat: string, flags: string, info: dict<any> ): any
+      g:LocalTagFuncArgs = [pat, flags, info]
+      return null
+    enddef
+    &tagfunc = s:LocalTagFunc
+    new
+    g:LocalTagFuncArgs = []
+    assert_fails('tag a12', 'E433:')
+    assert_equal(['a12', '', {}], g:LocalTagFuncArgs)
+    bw!
   END
   call CheckScriptSuccess(lines)
 
@@ -344,13 +389,4 @@
   %bw!
 endfunc
 
-func Test_set_tagfunc_on_cmdline()
-  CheckScreendump
-
-  let buf = RunVimInTerminal(' +"set tagfunc=s:Func"', #{rows: 6, wait_for_ruler: 0})
-  call VerifyScreenDump(buf, 'Test_set_tagfunc_on_cmdline', {})
-  call StopVimInTerminal(buf)
-endfunc
-
-
 " vim: shiftwidth=2 sts=2 expandtab