Let me try to break it down the best that I can :) Remember this is my general belief and others might feel differently, but this seems to be how most of the people around me feel about this as well! β€οΈ
So there is nothing wrong with giving yourself a Korean name if you need it for convenience. If you're travelling to Korea or interacting with a lot of Koreans and need a Korean name in order to make things easier, yes do it! But I do think that as someone who is not Korean, you should maintain the name as kind of similar to your own name (so it's obvious that it is out of convenience and you're not just giving yourself a name as a fashion). π
For example, your name is Elizabeth: you can make your Korean name:
λ¦¬μ¦ (liz) or μ리 (eli) -- not straight up naming yourself νμ (HYUNA) or something. You know what I mean?
As many of you know there are a lot of people who fetishize Korean culture and Korea in general and I hope you guys remember that there is a culture and a history of people behind the language you are learning :) It isn't just a trend or a fashion but there are real people who are behind the names! SO, I'd say, give yourself a Korean name (like the one above) but don't give yourself a Korean last name. As I've said before, Korean last names are tied to family lineage so I'd steer clear of doing that β€οΈ
Hope that helped! Have a great week everyone :)