I have a game and I would like to change my name as GM, can I do that once the game has started?

You can...I would imagine it's done the same way as changing any other character name.  I'm in a game where the GM (who's also providing a major NPC in the game and therefore just used that character's name) got promotions, and has gone from Commander to Admiral, and changed his name for that.

Dammit, why didn't I think of that!

But yes, easy to do. GM menu in the upper right, Edit Characters (second from the top) pick your GM name, and change it, super easy.