Many other StackExchange sites have a logo on the traffic page. How can we go about getting one of our own, as opposed to the default blue chatbox and M we have now?
Monero Stack Exchange is still in public beta. A site goes through several stages from proposal, definition, commitment, private & public beta, to finally the graduation (explained that on reddit a while ago).
We are currently in public beta, this is the last and most important step before graduation. Your follow-up question will be probably, what do we have to do to succeed and graduate? It basically breaks down to a strong community both in terms of active users and frequently questions asked per day, about 10 per day on average.
Custom site themes and logos will be applied after graduation.