Picking and sticking with a name is definitely different for everyone.
I'm one of those people that firmly believes that you don't 'choose' the name, but that the name chooses you (A little like Pokemon, if you will)
When it came time that I wanted to go by a different name (Even though my birth name is rather androgynous) I knew that I didn't want something too similar to my birthname, but I did know that I was more inclined to have my first name start with a D because my father's name is David, and my grandfather's name was Delmar, so it seemed very appropriate to stick with a D, though I wasn't hell bent on it.
I made a list of names from sites that I found (babyname sites, of course) and then I went to a forum, posted a picture and asked for opinions. I tried going by a few of them; I really like Derrick, Ethan, Evan, and a few others, I tried then, but they didn't fit. They just didn't feel right, when people used them, I didn't realize that they were talking to me. But then I tried Darius, and the first time someone used it, I looked right up and I knew that that was me. I get a lot of crap over it, believe you me, because it's traditionally a Black name (African American, to be politically correct, if you insist) and I get over jokes over it ALL the bloody time, because I am painfully white. I've thought about changing it, but when I look I myself in the mirror, I go... "Nope, I'm Darius," And it's going to stay that way.
When it came to middle names, I went by Aiden for about a year. Darius Aiden. I wanted an A because my mother's last name is Andersen. But then I realized that every other transboy used Aiden as a first or middle name, and I wanted none of that. So I was back on the hunt again. I kept looking for an A, but didn't like anything that I came up with. So I started looking for other names that I hadn't thought about. At that time, I was really...painfully obsessed with Criminal Minds, and Matthew Gray Gubler, who plays Spencer Reid. My mother constantly compares me to Spencer, because I tend to rattle off bizarre and highly unknown facts like he does, just about all the time. So I played around with Darius Spencer, Darius Reid, and finally...the one that stuck, Darius Gray. I decided to keep it as 'Gray,' and not 'Grey,' namely because of the A, and also because 'Gray,' is the more 'British' spelling of the word, and I have ancestors from England, and wanted to pay homage to that.
For my last name, I took my birth name, and used that, so my first name is going to become my last. It's the first thing that I received coming into this world, so it's always going to be important to me, and I want it to be a part of my life.
I put a lot of thought behind all of my names, but for some people, it doesn't take all this thought. Just go with whatever feels comfortable.
Good luck there, mate!