If you have a valid NY license, permit or ID card, you must bring your original social security card or W-2 with full SSN. This name, as it appears on your proof of identity, will be displayed on your card as required by federal law. “You MUST bring to the office the following original or certified proof documents: For example, here's what the New York DMV website says is required for a REAL ID: Getting a REAL ID or EDL requires additional paperwork, which you can find on your state's DMV website.
The bad news: You need to visit a DMV office to do it and you may need to plan ahead. The good news: If your license is not REAL ID compliant, you've got about 18 months to get an updated license.