Names are important, but they're also something which quickly vanishes into the background. They are symbols. Once we learn someone's name, or get used to the way a certain person addresses us (whether it's our full name if our parents are angry at us, a nickname on the playground as a kid, or 'boy' from the middle-aged shopkeeper at the corner store) they stop being words or even sounds, and start being symbols.
I began to realise a few years back back that some of my friends called me 'Ro', a shortening of my birth-name. This was mostly interesting because I quite genuinely had no idea who did it. I had to think very carefully to figure out who did it as a matter of course. My brain heard that noise and translated it to 'someone is addressing you'.
I mention this because names took on a very different meaning once I began transitioning.
First, there was the strange experience of selecting a new name for yourself. Lots of us get to pick a name, but only in a round-about way - we choose to prefer our name shortened, full, or using some specific abbreviation. My grandmother hated her first name (Hilda) so much she went by her middle name for her whole life. So in that way, selecting a name for ourselves is not that uncommon - for most of us it's just less of a blank slate.
The decision to change your name when transitioning is, obviously, very personal. Some people I know with gender-neutral names kept their name; others changed it regardless. For those with a very gendered name, it may seem like there's little choice.
I was a bit stuck - I love my birth-name. Heck, my parents named me 'Rohan' after Lord of the Rings, and I don't think there's anything cooler than that. (Also, I'm glad I became Rohan and not Gondor or Gimli.) But it's pretty masculine. There are feminised versions, but none that felt right.
And more than that, changing your name serves a second purpose when transitioning or making any major life changes - it's a symbol. On some level, my birth name represented a personality I had carefully constructed to service 'acting male'. So on some level, as long as I was 'Rohan', I was going to have difficulty changing learned and unhealthy behaviours.
I knew I had to change. So... picking a name.
In my case, I had a name in mind since I was about 12. Back when I didn't understand any of this, but knew something was wrong, I remember cautiously asking one of my parents what I would have been called if I was a girl. The name I heard was some variation of 'Elissa', and so I spent years as a teen day-dreaming about what Elissa would be like, and how much happier she'd be than Rohan.
And I was right.