As a rule of thumb ... change your name with the SS administration FIRST ... once that is done, using the marriage certificate & the newly minted SS card you can then get your DL, bank account and any other things changed over.
As for the W-4 at work ... if the boss changes your name on the paycheck before you change it at the bank then the checks may not be negotiable ... check with your bank. AND read the 4 page W-4 worksheet carefully especially if you both work ... most times both of you cannot claim married without owing at the end of the year. I highly recommend neither of you change the withholdings until you really do the math ... in my 25 years of experience only one of you can be on the married chart and the other ( usually the lower wage earner) should remain as single for withholding purposes and YES that is allowed and in most cases encouraged.
