Definitely-- The first "Tent server implementation" will have it's own name, TBD. We spent a lot of time on nomenclature and still aren't 100% with any of the terms, they're effectively all in flux until v1.0. The wackier issue is whether users call their "Tent-servers" "Tents". If you have any suggestions on names for this or any other terms, we'd love to hear them!
edit: when the hosted version launches it will be on a different domain, to make clear tent.io is the protocol alone and we aren't monopolizing the hosting space (we're doing it more as a community service than as a business).