I have doubts about the name of the game they created and about the name of the

I have a question, if, for example, at the time of finishing the development of my game, the name would obviously be the trademark of the game, should I register the name as a trademark? I have never thought about this, that is why I want to clear up all my doubts, if so, of having to register the name of my game as a trademark, where can I do it?