All that is needed is to compare the the worksheets' names using loops:

[vba]Public Sub UpdateMe()

'Sourcewb refers to the workbook where the data is stored;
'Targetwb refers to the workbook where data is going to be pasted into
Set Sourcewb = Workbooks("Book1")
Set Targetwb = Workbooks("Book2")

For Each SourceSheet In Sourcewb.Sheets
For Each TargetSheet In Targetwb.Sheets
If SourceSheet.Name = TargetSheet.Name Then

'Rest of the code follows

End If
Next TargetSheet
Next SourceSheet

End Sub[/vba]
Of course, I think you may need to amend your original code so as to fit it into the loop. The code is kinda lengthy and I've saved it in the attached file. Check it out for the actual changes I did.