Was able to update name and gender at social security today. Am I good?

I went into my social security appointment in Los Angeles today (2/6/25) hoping to at least change my name so I can update my driver’s license. I brought my court order from California granting a name and gender change from last year. The clerk showed me the final receipt with the updated info and I noticed that she also updated my gender according to my court doc. I asked about the emergency order and she said she wasn’t given any instructions. She said to expect my new social security card in the mail in 10 days. Am I good now? It was so easy. She didn’t ask any questions. Or does the application require additional approval?