That's up to you. Trademarks arise from use in commerce. You get certain trademark rights just because your game was brought on to the market. Registration may give you additional protection. Registration is allowed if you have the "intent" to use in commerce (though you need to actually have done so to protect he mark).
In either event, you should make sure you are using a defensible mark (not descriptive, etc...) and certainly one that isn't likely to infringe on an existing mark.