Cycle through sheets and drag down formula - Not working

I've got a bit of code that puts the worksheet name in cell C2 which works perfectly for all sheets.

I then want to drag this down depending on how many cells there are in cell A, again for all sheets. This doesn't seem to work, it does nothing.

Any ideas?

Sub SheetName()


    
    
    For Each ws In ActiveWorkbook.Worksheets
    
    If ws.Name <> ActiveSheet.Name Then
    
    ws.Range("C2").Value = ws.Name
    
     
    Dim LR As Integer
     LR = Range("A" & Rows.Count).End(xlUp).Row
     Range("C2").AutoFill Destination:=Range("C2:C" & LR), Type:=xlFillDefault


    
    
    End If

    Next

Thanks

This works for me.

Sub SheetName()

    Dim LR As Integer
   For Each ws In ActiveWorkbook.Worksheets
    
       With ws
            If .Name <> ActiveSheet.Name Then
            
              .Range("C2").Value = .Name
            
              LR = .Range("A" & .Rows.Count).End(xlUp).Row
             .Range("C2").AutoFill Range("C2:C" & LR), Type:=xlFillDefault
        
            End If
       End With
   Next
End Sub