what is the name of the loan ,, where several family members can sign up for the 1 morgage?

It's a joint mortgage, which is different from a joint title or joint deed. Make sure you have a lawyer draw up an agreement laying out exactly what everyone's responsibilities are in the event someone dies, goes bankrupt, marries, moves, gets divorced, defaults on the loan, wants to sell, any problem at all. This is separate from the mortgage document or the deed. If you don't, you WILL find yourself in court with your family one day.

I would call that a problem and the makings of family discord. Do not do this without legal advice. Multiple ownership/debt things can work but 9 times out of 10 they don't. And you really don't want to be feuding with your family about money.