How/when to bring up my name change and absent father to new gf?

I took my mom and stepdad's name in the last month, having it legally changed from my birth name. However, at 20 a lot of people would be surprised that I would do it considering that is something you normally do at a younger age. Anyways, My mom warned me this would be a conversation that I would have to have from now on, but I just don't know how to go about it or explain it. It isn't an unwillingness or denial thing.

I have always wanted to, but never had the money until I saved up enough from my tips from waiting tables at the Chili's I work at this past/current school year. I did it because I basically don't have anything linking me to my biological father's family other than the last name. They are all stuck up and prudes. My father himself is absent and never really was there for me as a kid. My stepdad basically stepped in very slowly and became my "dad" even more whenever I got in my later teens.

I was wanting advice though about how to explain this to a girl that I am out with and like about this to where it isn't telling your lifestory and not just "because I wanted to," in fear of seeming smug. I mean, it wasn't an act of wanting to divorce myself or whatever from my father. I honestly don't give a crap about him not being around anymore. I haven't talked to him in like 4 years. He has been out of my older brother's life and talked as if he was dead for the last 10 years; my bro is 8 years older than me. I just want to live my life and he isn't a good influence or parent. (Buying me alcohol/slipping me a drink at restaurants and stuff, would let me have girls over and let them stay the night whenever I wanted at his house, etc.) I did this for me not an act of getting back or anything like that.

I just don't know how or when it would be a good idea to explain what happened. I don't wanna come off as being dramatic or something like that.