I guess I'll answer this, and probably get downvoted because of a certain game that I'll mention.
The "A Noob" part of my name dates back to when I used to play Roblox (pls don't hate me for that lol, I stopped playing it two years ago). In late 2017, I really wanted to change my username, because my old one had started to make me cringe and question what I was thinking (and I will not mention it here), and I began using the Noob skin, forming a Noob Gang among some friends. Two months later, I saved up enough to get my username changed to "JustAnElementalNoob", referencing my favourite Roblox game at that time, Elemental Battlegrounds, and that fact that I still had the Noob skin, except with cosmetics representing fire, ice and electricity. About a year later, I stopped playing Roblox.
Then the "Without A Name" part of my username. In April 2019, which was around the time I lost interest in Roblox, I started playing Pokémon Showdown. I didn't really know what to make my username. Even if my Roblox username didn't go over the character limit (which it did) there's no way I would've went with it. I wanted to keep the "Noob" part in, but had no idea what else to put in my username. Eventually, because I couldn't think of a name, I settled with "ANoobWithoutAName". That name has stuck with me since.
Ever since I created my Showdown account, every username I've made since then have been either the same as it somewhat similar to it, depending on the character limit. Part of the reason it's stuck with me is because of the potential for jokes. I remember once while I was playing something, someone said to me: "I'm gonna call you Billy" (I don't have a screenshot sadly), and Frozen Inferno 火 has already made a few jokes about it, including but not limited to this:
When you become a AHaxerWithoutAName XDD
commented Mar 26 by Frozen Inferno 火
So, yeah. That's how I got my username. I'm not very creative so it's likely that I'll never change it. If one day I do change my username, it'll probably be something related to The Legend of Zelda: Twilight Princess, my favourite video game of all time. But no guarantees.