The W-2 has no direct correlation to your debit card. You should file with the name that social security has you listed by. If you changed your name due to marriage and have not changed it with social security, leave it the way it is on your return despite the W-2.
If you have changed your name with social security, use your married name. The only likely circumstance will occur if someone needs a form of ID to prove ownership on the debit card, such as your license. If have run into this scenario before, (I never have) be sure to have an ID that matches the name on your credit card.
