Here's my opinion (and I'm obviously in the delusion that everyone cares, thx anyway) The Sonic Center sounds a little like some generic Sonic site that would be just as much about the fandom and art and Satam and crap than it would be about time attacking. So changing the naming is a reasonable idea, although we don't have to.
And as for the names like "Time Up" and "Time Over" they only imply time attacking, not score and rings which this site also has, but THERE IS NOTHING WRONG WITH THAT. It's fashionable to have non-implied encompassing names. Besides, we all know time attacking is the most emphasized aspect here.
Act 1 or Act One sounds better than First Act. In any case it's a good name even though the 3D games don't have acts.
Probably the best name is something straightforward. There's gonna be confusion no matter what unless it has the word Sonic in it. After "Sonic" we should just say what this site is about. Sonic Rankings for example.