In my experience, if a job application asks specifications for my legal name ( I haven't changed it yet, procrastination) then I use my birth name. If it doesn't, then I use my chosen name.
Last year I worked for a car dealership, and when I applied and interviewed I was known only as my chosen name (I was only about 5 months ish on T). I was hired, and when filing out the paperwork in the HR department I made sure and told the lady in charge of HR that my legal name was different, as they need to take copies of your photo ID and stuff. Never once did the word "transgender" come out of my mouth and no one asked questions. My coworkers didn't know, my boss didn't, nothing. It's not their business.
Recently I had a job interview at Dicks sporting goods, and since their application requested legal name, the manager who interviewed me initially referred to me as such. I just politely told him that that was my legal name, but I went by (insert name here). That was it and he was respectful about it.
