This may get you started:
Option Explicit
Sub testme()
Dim myFileName As String
Dim myExt As String
myFileName = ThisWorkbook.Name
'find extension
myExt = Mid(myFileName, InStrRev(myFileName, "."))
'strip off extension
myFileName = Left(myFileName, InStrRev(myFileName, ".") - 1)
'Check last x characters for date format
If Right(myFileName, 11) Like "_####-##-##" Then
'strip off previous date
myFileName = Left(myFileName, Len(myFileName) - Len("_####-##-##"))
End If
'add date
myFileName = myFileName & Format(Date, "_yyyy-mm-dd") & myExt
With ThisWorkbook
If myFileName = .Name Then
'same date, just do a save
.Save
MsgBox "Saved using same name"
Else
'don't show overwrite prompt
Application.DisplayAlerts = False
'save as new name
.SaveAs Filename:=.Path & "\" & myFileName, FileFormat:=.FileFormat
Application.DisplayAlerts = True
End If
End With
End Sub
I used a date format of: _yyyy-mm-dd
I find that it's easier for sorting and the underscore makes it easier to read.