Here are some important things to consider when picking a name.
It can be tempting to want to use your real name, but for the sake of your personal privacy it’s best not to.
Your player name will be visible to players in your area when you found a Safe House or leave Survivors at one. When you join a Group everyone there will also be able to see your name.
Think of a name that’s easily memorable for you, and the more unique it is the better. With it you can stand out from the crowd and gain some kudos for rescuing the most Survivors, or founding lots of Safe Houses.