I don't hate the name, but I don't love it either. When you have a classic non-corporate arena name for all these years, anything would sound weird though. It'll get shortened by the fans though. The official name is the Little Caesars Arena, but everyone will just call it Caesars, which doesn't sound so bad.
Yeah...there's a problem with that...this is right across the river:
We're gonna have to call it the LCA or give it some other nickname.
I was at that game, so far he looks pretty decent. Good skater, definitely not afraid to take shots (only hesitated once in Overtime), broke up a few of Saginaw's offensive chances, played the point on the PP, and went 2nd in the shootout. Obviously one game isn't enough to figure out where he'll be going in the future, but he's definitely noticeable when he's on the ice, in a good way.
I don't think one's reaction to the result of a game necessarily has to do with being a fan or not. I think it relies more on if you like a team or not, and why. If you like a team because their name sounds cool or they recently won a Cup, you're probably at best a bandwagon fan until you educate yourself a little more and get invested to the point where you don't ditch them as soon as they start losing. On the other hand, if you truly care about how well they're doing and stick with them even when they're not adequately performing, then I would say you're a true fan. Reactions to games are just that, reactions, and nothing more. Different kinds of fans react differently. There's the overly pessimistic, the realist, the optimistic, the "homers", the ride the high's and berate the lows, etc. It takes all kinds to have a fanbase, otherwise we'd all have the exact same opinions and feelings and it would become very boring very quickly.