Macro to sort multiple columns in order, on any sheet/table

Below macro has been working great for me - but it's limited to only the table specified in the code. I've been trying to morph it to work in whatever table/sheet is active. I thought for sure my "ActiveTable" variable would work... What am i missing?

Before: (Works great, but only specified table)

Sub Optimal_Sort()
'
' Optimal_Sort Macro
'
Application.ScreenUpdating = False
'
    ActiveWorkbook.Worksheets("Processing").ListObjects("Table4").Sort.SortFields.Clear
    ActiveWorkbook.Worksheets("Processing").ListObjects("Table4").Sort.SortFields.Add _
        Key:=Range("Table4[[#All],[BL]]"), SortOn:=xlSortOnValues, Order:= _
        xlDescending, DataOption:=xlSortNormal
    With ActiveWorkbook.Worksheets("Processing").ListObjects("Table4").Sort
        .Header = xlYes
        .MatchCase = False
        .Orientation = xlTopToBottom
        .SortMethod = xlPinYin
        .Apply
    End With
    ActiveWorkbook.Worksheets("Processing").ListObjects("Table4").Sort.SortFields.Clear
    ActiveWorkbook.Worksheets("Processing").ListObjects("Table4").Sort.SortFields.Add _
        Key:=Range("Table4[[#All],[STNAME]]"), SortOn:=xlSortOnValues, Order:= _
        xlAscending, DataOption:=xlSortNormal
    With ActiveWorkbook.Worksheets("Processing").ListObjects("Table4").Sort
        .Header = xlYes
        .MatchCase = False
        .Orientation = xlTopToBottom
        .SortMethod = xlPinYin
        .Apply
    End With
    ActiveWorkbook.Worksheets("Processing").ListObjects("Table4").Sort.SortFields.Clear
    ActiveWorkbook.Worksheets("Processing").ListObjects("Table4").Sort.SortFields.Add _
        Key:=Range("Table4[[#All],[ACTUALSHIP]]"), SortOn:=xlSortOnValues, Order:= _
        xlDescending, DataOption:=xlSortNormal
    With ActiveWorkbook.Worksheets("Processing").ListObjects("Table4").Sort
        .Header = xlYes
        .MatchCase = False
        .Orientation = xlTopToBottom
        .SortMethod = xlPinYin
        .Apply
    End With
    Application.ScreenUpdating = True
End Sub

After: (Doesn't work )

Sub Test_Sort()
'
' Test_Sort Macro
'
Dim ActiveTable As String

ActiveTable = ActiveSheet.ListObjects(1).Name

Application.ScreenUpdating = False
'
    ActiveWorkbook.ActiveSheet.ActiveTable.Sort.SortFields.Clear
    ActiveWorkbook.ActiveSheet.ActiveTable.Sort.SortFields.Add _
        Key:=Range(ActiveTable & "[[#All],[BL]]"), SortOn:=xlSortOnValues, Order:= _
        xlDescending, DataOption:=xlSortNormal
    With ActiveWorkbook.ActiveSheet.ActiveTable.Sort
        .Header = xlYes
        .MatchCase = False
        .Orientation = xlTopToBottom
        .SortMethod = xlPinYin
        .Apply
    End With
    ActiveWorkbook.ActiveSheet.ActiveTable.Sort.SortFields.Clear
    ActiveWorkbook.ActiveSheet.ActiveTable.Sort.SortFields.Add _
        Key:=Range(ActiveTable & "[[#All],[STNAME]]"), SortOn:=xlSortOnValues, Order:= _
        xlAscending, DataOption:=xlSortNormal
    With ActiveWorkbook.ActiveSheet.ActiveTable.Sort
        .Header = xlYes
        .MatchCase = False
        .Orientation = xlTopToBottom
        .SortMethod = xlPinYin
        .Apply
    End With
    ActiveWorkbook.ActiveSheet.ActiveTable.Sort.SortFields.Clear
    ActiveWorkbook.ActiveSheet.ActiveTable.Sort.SortFields.Add _
        Key:=Range(ActiveTable & "[[#All],[ACTUALSHIP]]"), SortOn:=xlSortOnValues, Order:= _
        xlDescending, DataOption:=xlSortNormal
    With ActiveWorkbook.ActiveSheet.ActiveTable.Sort
        .Header = xlYes
        .MatchCase = False
        .Orientation = xlTopToBottom
        .SortMethod = xlPinYin
        .Apply
    End With
    
    Application.ScreenUpdating = True
End Sub

Is this even the best way to sort these 3 fields in this certain order? The help is much appreciated.