Beware of naming yourself anything from anime, manga or trading cards, as they have little connection with reality or everyday life in Japan. If you would happily take a nickname (aren't nicknames usually given to you by other people anyway?) from an American cartoon or comic, then by all means, go ahead.
There is nothing wrong with the name Jenny though, if that is your real name, and Japanese people will have no problems pronouncing it.
If you give yourself a Japanese name, expect to be constantly asked "Why?"