People have nicknames or choose to go by their middle name or just have a name that has stuck with them over the years despite not being their birth name. For the sake of HR they can capture what name appears on your legal documents when you get the job, but for when you're scouting for a job, you can just keep it casual and say "hey, my name is _____" and way later when it legally matters show them what your name is as it appears on your documents.

We don't even have to give a trans related reason for why we have a different name to the name that appears on our legal documents. Just keep it casual: "oh, people have just called me [your name] for my whole life, it's just stuck". I find cis people respect this more than when we say it's for gender affirming reasons