How do you get your nametag to have color when you are in multiplayer?

Buy a "user name" item, there are available in any colour in the shop/market.

^ this person is wrong, its called a "user text" item.

secondly, the user text item makes your name (when playing) in the top right corner a different color, if you are talking about a colored name in the chat area then that is related to begin a GM or admin of some sort. GMs and Admins will have a red name, normal users have a blue name, Unibash and trial GMs have Yellow names, and the Operator of the server has a green name.