If you are getting a gold star added to your driver's license and the name you are using on your driver's license matches your passport or certified birth certificate, you do not need to provide any additional name information. If it does not match, then you would need to provide a certified marriage certificate or court document to show the name change.
I'm not a DOT expert at all but I don't think they have ever asked me if I'm married or not. So I THINK it shouldn't cause an issue. As long as you have a few forms of verification with that name I think you will be fine! At the end of the day... I'd call them though!
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