Andy seems to have covered most of the bases.
Still, here's my 30 cents worth - you guys really have to sit down and discuss this and discuss, as Andy points out, all the other costs that perhaps you have not thought too deeply about, like replacement costs, contingency costs, service and repairs, heating, lighting, insurance.
Possibly the best is to just divide the costs by the time spent in the studio. And if one of you guys books it and does not end up using that time, I would say 'Tough! You still have to pony up your part of the costs, including time booked but not used!'
As for identity - give the animal a name!
As you can see, we have a studio, built on the site of an old cattle byre, so we called it The Byre. If it had been an old factory, I would have called it The Factory - and so on. Give it an identity that people will be able to relate to and leave it at that.
The identity of the studio is very important and I would avoid diluting it with other names attached. Getting a level of recognition is hard enough as it is, without customers getting confused by daft add-on names. They'll realise that there are three separate companies using the one facility when they ask for the invoice!
Oh, and good luck BTW!