If we limit the analysis to video games, I would feel comfortable saying yes. (Because video games are generally not limited to a certain geographic area). As a countr example (I think it is Pizza Hut) there was a small mom and pop brick and mortar resturant in a small town that predates the multinational corporation, The mom and pop do not need to change their name but they can not expand.

*it is best not to answer legal questions generally, the answer will always be: maybe. A legal analysis must be done with specific facts