I think it depends on the scope of the place and what you are promoting and/or selling. What I mean by this is, is it a coffee shop and/or a bar? What is the extent of the gaming part of it? Is it mainly a bar with a few computers on the side, or is it computer dominated with a bar/barista on the side? Are you catering to computer gamers or say the xbox console/kinect audience or add some arcade games into the mix? How big is the place? Big enough to say, 1st floor be under 21 with a 2nd floor 21+. Are you going to try, for example, to hold gaming tournaments and bring people in? Or things like MLG gaming sanctioned tournaments?
What I mean by all this, to figure out the concept you are going with and then structure the name around it. Thus Leeerooyy Jenkins Gaming Lounge definitely would define a concept and say what it is.
Personally, if I were to do a gamiong bar/cafe/lounge, I would structure it around tournaments. You have to offer something that someone just can't get sitting on their ass at home. Thus something like LAN based Starcraft tournaments, I would also do some console based tournaments, especially sports gaming. Add that if you did this, I'd also suggest having a stage where you could mount of a coiuple of front projectors and show the finals or feature round, kind of like WSOP's feature table.
Which also brings me to 2ndary thought, have gaming tables, meaning poker tables, having a few of those and holding poker tourneys is a great way to draw people in as well. Most states, if not mistaken, allow for pay to play poker tournaments as long as the house isn't taking a rake.