When a person is baptized, why do they change their name?

Do they actually use this name? by actually legally changing it? I am a bit confused. Please explain this. Do we tell people at church we are the saints name we chose or our birth name? I don't get the idea of why they do this and is it just like a confirmation thing only? I am illiterate but will check your answers. The most detailed will get the points. Good luck!