My father's name on my birth certificate does not match the name on my social security card (Mom signed my sister and I up for SS with step=father's name, but he never legally adopted us.)
I've used my step-father's name my entire life. In common law, you can change your name by usage. It was never a problem. When the discrepancy came up, an affidavit was always fine. Until 9/11 that is.
NJ had some sort of "enhanced" driver's license requirements after 9/11. I went through the process to get a court-ordered name change. A major pain and expense (paying filing fees and paying to publish three rounds of public notices of the change from a name I had never used to the name I've always used). Unfortunately, I fucked up. The order I got from the court was a preliminary order. One more round of publishing a public notice was required to get the final order. I didn't understand this. The DMV accepted what I provided and issued the license. I didn't find out it wasn't a final order 'til I sent it in to get the name changed on my birth certificate. By that time, I'd missed the deadline and would have had to start the whole process over. But I had a valid license, so I said screw it. When I moved to WA they just took the NJ license as proof.
The process to get a name change here is WA is simpler, but it takes most of a weekday to file the papers and sit around to be heard by the judge. It was actually just about impossible for awhile because they were swamped with people who had to get a legal name change to get a REAL ID last year. I've got to do it, but these days I run a little solo dog walking service and just haven't been able to take a weekday off.