The main site, is very outdated. But the best place to check for competing events is here.
A thread will start like: new comp event.
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You would then sign up. You might put a team name, a logo etc.
Most events don't ask for the names of everyone involved but maybe a couple of points of contact (to invite into game and other organisational things.)
As its Christmas not a lot is happening. But a good especially if you're new to the competitive scene is SCS or Sunday community skirmish. It's a weekly knock out tournament kind if thing. You simply sign up in the thread with a team name, and you're. good to go. Note that competitive didn't allow for single player sign ups, you need to sign up confident of having a full team. (8 players usually.)
Other than this there are other events with matches usually held on Saturdays, events can span for weeks, so you have to make sure you can give up the time.
Hope that cleared some things up, if not ask more questions
Dammit geo, got in before me. I'll post anyway, cos I typed this all on my phone :p