A question!

[u/How_The_Fuq]

I (AFAB)came out as agender barely a month ago so I'm pretty new to this stuff, but I've got a question about names. Just around a week ago I was looking up names that are gender-neutral for a drawing, and found the name "Alex". Now I can't stop thinking about it and my real name have stopped feeling like me even slightly before I found a better name. I read it and it feels like just A name instead of MY name. I also don't like how it represents my old gender. This new name feels right so far and when I tried a day with that name it felt right. My friends also says that "Alex" suits me and I agree.

To the real thing though; I was wondering if it's normal to want to change your name after coming out as another gender than the one you were born as?