Xbox LIVE title, how about. Oh wait, it's microsoft. "Xbox LIVE Gamer title"
Why would you call the entire section "Xbox LIVE Title". That makes no sense.
All companies name stuff, for example "PSN". However, sometimes more creative names than "<name> Store" arise due to a process called marketing. Making a unique name for something is a good way to get recognition. XBL Arcade is more appealing than "Xbox LIVE Game Store" to people. Everything does this; This is why a Big Mac isn't called a "Burger with two pieces of meat and 3 pieces of bread (with other toppings as well)" and Wendy's "Frosty's" over "Soft Serve Ice Cream in a Cup". You're not even criticizing Microsoft in specific, it's more like you're trying to point out a fallacy in businesses in general.
I don't even know what you're referring to in the second part there, but I think you're thinking "gamertag"?