I never really went by my birth name, not even my parents called me that, they called me a totally different name, and my peer group as a teenager called me a third name, and my friends online knew me as a forth name, so I found it pretty easy to wear a new name lol
As for choosing one, I wanted some connection to my family, but not to really be directly connected with it, so I made my name an anagram of my mothers name, and changed my last and middle names to names I liked, even if they were more popular in the late 1800s than now. I did have to explain to the judge my I wanted to change all of my names rather than just my given name.
Obviously, you can't really make but so many names with anagrams, but my advice is to pick something that has a connection to something important to you, and you like. It doesn't really matter so much, unless ofc you are young and trying to get started in a career, then statistics say names might have a pretty big effect on your resume, with names that sound ethnic or even just strange tending to be skipped over. That would be the only real reason not to just pick whatever.
Also try not to waver, when you pick something stick with it, people will be difficult with you many times if you waver at all, and that isn't fair, but it does seem to be how people are.