After hunting through various snippets of code, I have done this:

Dim sNewFileName As String

sNewFileName = ActiveDocument.FullName
sNewFileName = sNewFileName + ".txt"

Then, where the file is saved, instead of:
ActiveDocument.SaveAs FileName:="1.txt"
I have:
ActiveDocument.SaveAs FileName:=sNewFileName

These lines get the current file name and add the extension ."txt" to it.

At this stage, it looks messy, cos the file is then saved as "1.doc.txt" but I have a small freeware package that does batch file renaming, so it's easy to strip that ".doc" from it.

So, the whole macro (including convertin it to text and closing the window), now looks like this:

---
Sub SaveAsText()
'
' SaveAsText Macro
'
'

Dim sNewFileName As String

sNewFileName = ActiveDocument.FullName
sNewFileName = sNewFileName + ".txt"

Selection.Rows.ConvertToText Separator:=wdSeparateByTabs, NestedTables:= _
True
ActiveDocument.SaveAs FileName:=sNewFileName, _
FileFormat:=wdFormatText, LockComments:=False, Password:="", _
AddToRecentFiles:=True, WritePassword:="", ReadOnlyRecommended:=False, _
EmbedTrueTypeFonts:=False, SaveNativePictureFormat:=False, SaveFormsData _
:=False, SaveAsAOCELetter:=False, Encoding:=65001, InsertLineBreaks:= _
False, AllowSubstitutions:=False, LineEnding:=wdCRLF
ActiveWindow.Close

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