If there's a bookmark in table 4, the code can be simplified e.g as below, where I have also provided different options for each of the four tables if required.
Code:
If ActiveDocument.Tables.Count > 3 Then
If ActiveDocument.Tables(4).Range.Bookmarks.Exists("bmName") = True Then
For i = 1 To 4
Set oTable = ActiveDocument.Tables(i)
'Do something with otable e.g.
Select Case i
Case Is = 1
oTable.Cell(1, 1).Range.Text = "Test"
Case Is = 2
oTable.Cell(1, 1).Range.Text = "Test2"
Case Is = 3
oTable.Cell(1, 1).Range.Text = "Test3"
Case Is = 4
oTable.Cell(1, 1).Range.Text = "Test4"
End Select
Next i
End If
End If