VBA Subscript out of range error when saving file?

My advice to you is as follows:

declarate global variables in standard modules like

    Public wb As Workbook
    Public ws As Worksheet
    
    Sub startupSettings()
        Set wb = ThisWorkbook
        Set ws = wb.Worksheets("Sheetname")
    End Sub

you can call this procedure by worbook open event in thisworkbook code like

Private Sub Workbook_Open()
    startupSettings
End Sub

or every time as first when you lunch procedures

Sub someSub()
    startupSettings
    '.... code
End Sub

then your save file procedure looks like

option explicit

Sub saveMyFile()
    Dim path As String, fileName As String
    startupSettings '   if variables not set before
    Application.DisplayAlerts = True
    path = "S:\Common\Central\"
    fileName = ws.Range("A7").Value
    wb.SaveAs path & fileName & ".xlsx" ' if you save workbook with macro that line return error should be .xlsm or another procedure with workbook.add
    wb.Close
End Sub

Backup Workbook

• If you turn off Application.DisplayAlerts before saving, you won't see any dialog (overwrite, file format,...) and the file will be automatically overwritten. Don't forget to turn it on again.
• When saving files, you should always use a parameter for the second argument FileFormat. In your case, it is xlOpenXMLWorkbook for .xlsx files.

The Code

Option Explicit

Sub backupWorkbook()
    
    Const FolderPath As String = "S:\Common\Central\"

    Dim wb As Workbook: Set wb = ThisWorkbook ' workbook containing this code
    ' Set wb = ActiveWorkbook ' any workbook that is selected
    
    Dim BaseName As String: BaseName = wb.Worksheets("Fname").Range("A7").Value

    Application.DisplayAlerts = False
    wb.SaveAs FolderPath & BaseName & ".xlsx", xlOpenXMLWorkbook
    Application.DisplayAlerts = True

    wb.Close

End Sub