For me Its quite simple. My brain decided it. Literally. The days I found out I'm trans, my brain would do this weird thing, where I could think about completely different stuff and suddenly my now chosen name would "fly" into my mental Field of View, like an asteroid in star wars or so. I told that name a close friend and 4 weeks later when we went to the club together I told him, that I will stick with it, because I didnt had a better idea (and it was the only name I really felt comfortable with).
I had priorities and did research. I had rules I decided from the beginning. It took months to decide I even changed my mind a on somethings at the last minute
Initials I needed something to match my initials. That only changed slightly when I decided to make sure I didn't have my sperm donors last name.
I needed my name to come from a similar part of the globe historically. I think nowadays I'd have done the same thing for different reasons. When I first made this rule I'd done it to respect my sperm donor despite everything. Then later on I kept it because I had already decided on this and it filtered out thousands of names. If I had to name myself today, this rule would mean that my name comes from the same area as my siblings, which honestly means it doesn't stand out.
I needed the meaning of my name to matter. And I wanted something I'd always agree with. Personally I feel like I fucked up here. At the time I was extremely angry at my father and part of my name reflects that. Nowadays I wish I had picked something that embodied myself and wasn't just an insult towards someone else. I don't hate it but I feel like if I had gotten a second opinion I'd have gone with my other choice for a middle name.
It needed you sound a certain way, I needed saying first into middle to sound good. Not hard when they're from the same region but that's not always the case.
I think with this I only struggled to choose between 4-5 names and was going to put the number 2 or 3 pick as a middle name it worked out well for me. I think if I hadn't gotten pissed off during the time before I legally changed my name I'd definitely have a different middle name though.