I've never been called my name in real life yet, so it doesn't seem 100% solid yet, but Alex is what I wanted to get people to call me when I was younger but was always too shy to enforce. I like the idea of a name that I can shorten because I always wished I had a birthname I could shorten (probably because most shortenings sound more masculine than the long versions, but it kinda stuck), and as my birthname starts with "Z" I felt like that was the end, so my new name should begin with "A" as it's a new beginning.
My middle name, Luke, is what I told people was my middle name in primary school because I felt left out that I didn't have a middle name at all and they all had at least two each. I still feel different when people talk about middle names because I'm not out, and so don't have a middle name per se, so it felt important to have one this time around. I might also include Matthew as a second middle name because that's what I would of been called had I been male -- I considered it for a first name and quite like it, but I know too many Matthew's to be comfortable with it. I know plenty of Alexs as well, but it doesn't bug me the same way for some reason.
As for last names, there was never any doubt that I'd change that one day. Most people can't pronounce it to the extent that I doubt whether I'm saying right, and it's a pain in the rear to explain how to spell (Me: "It's 123, 123, 45" Them: "Was that 12345?" Me: "No, 123, 123 again 45. Two 123's.") I was thinking about what I would take, surnames mean a lot more than first names to me, although family means little, and then I was thinking about how one of my teachers had shown me more about family in one year than mine had in my whole life, but his surname didn't fit with my name at all. Running off that idea though I thought about "Petersson", literally meaning "Son of Peter", which although it isn't accurate in blood terms, is right in other ways, which IMO are more important to building a person than flesh and blood (which as we all know goes wrong sometimes).
So in it's entirety I'm Alexander Luke (Matthew?) Petersson. They're all pretty popular names for someone of my birth year as well, all above 14th in popularity. The meanings of the names didn't really come into it at all other than for Petersson.