I had practically lived full-time for months when I changed my name legally, and I changed it mainly because I felt it was time to come out to "everyone" (I was already out to close friends and immediate family), and I had planned on doing both at roughly the same time. If some people resisted the change, I would have the added argument that the new name actually is my name, look, it's on my passport... Now I'm not sure it would have changed their minds, but thankfully I have yet to meet anyone who insists on the old name.
Additionally, I had experienced an increasing amount of awkward situations when store clerks and so on needed my name or ID, and I stopped using my first name and pronouns at all in social settings. Obviously, being name- and pronoun-less is impractical and (at least in my case) self-erasing. So after a while, my psychologist hinted that perhaps changing my name would make things easier for me. Also, a female friend who I met in November told me she had always read me as a woman, and agreed with my psychologist that changing my name was a good idea. My parents also acknowledged this, after seeing me just weeks before. So basically I trusted them and went ahead with the name change. The legal change was approved within a week, and then a week later I dropped the bomb on Facebook, after my dad had informed my extended family.
So for me, I changed it at the point of coming out, but at that point I was also full-time; I didn't have a single male piece of clothing in my wardrobe. Additionally, I was at a point where my old name was not only a source of dysphoria, but of practical inconvenience, and where a female name would make things easier practically as well as emotionally.
