I would assume all hospitals have varying processes. You should ask your doctor or hospital.
Your doc will reserve a room if you are having a planned c-sec , that's what mine did and they did it when I was 28 weeks they won't do it any earlyer than that.
I don't think u can just after u have the baby they set u up with a room in know at my hospital they have a suite that u can get but only if it's available when u deliver and unless ur getting a c section and sometimes not even then will u know ur exact date! Ur due date is just a guess! So for ur answer u might need to contact the hospital u will be delivered at!
You don't technically have to register. They won't turn you away when you're in labor. Registering wasn't a big deal at my hospital. They basically just get your insurance info, your name, job and drs name. I registered at 36 weeks but was told it wasn't necessary.