My brother changed his first name. He did not have to change his middle, though I was completely surprised he didn't.
I don't think he had to change his birth certificate...the name change documents show the paper trail...then again, his was a change from his name to a nickname that he wanted done formally so the Air Force would stop bringing up his "old" outgrown name whenever they wrote him.
He did go through a lawyer...the lawyer was our uncle so there were no lawyer's fees, but they just paid a certain amount to announce something in the paper for a certain period of time, then whatever official things there were. Few hundred bucks, I think...our mom was against it (she's the one that originally named him) but she probably paid for it, and she would have balked if it had been more.
It was hard on all of us, because for so many years he would get angry if we nicknamed him...then suddenly he was demanding this particular nickname. He's a very stern person who can freeze you out, and just like he did when we called him a nickname before, he just would NOT answer if we called him by his original name. He was so strict about it that he and his wife were together a few years before she knew that he had an old name (whoopsie, I told her).
He so completely rejected the old name that he wouldn't even tell you if he was happier...he'd just ignore the question b/c it's irrelevant. In that way I'd say he's happier.
I think my brother was 19 or 20, in college, he'd been using the name since he was 15 or so (but close family was "allowed" to use the old name by accident, LOL) when he re-made himself after a cross-country move...
I don't think it would make a difference of what age you are. If you're a minor it might be more complicated, because you would probably need parental approval for it. Once an adult, however, that wouldn't be needed.
I still think of my brother as his old name, though I never call him that anymore, it's been quite awhile. But to me, he IS the old name...and I know my mom felt like that always, and our dad (who has no contact with my brother) has never gotten used to the shorter name. I went many years hating my name (Molly), considered changing it many times, but once I saw what his name change did to my close family, I dropped it from consideration. Like it or not, it's who I've been since before I was born (thankfully I was a girl, b/c I would have been Oliver as a boy and I doubt I could feel positive about that...my mom just had unusual names for boys and better names for girls...my brother would have been Diana, if he'd been a girl, which is nice and strong) and I'm sticking with it.