Is it permissible to gift a house to a girl who is an orphan of both parents, in the absence of children?

There is no objection to writing the house in the daughter's name. If this is done with the intention that it becomes hers after the parents' death, then it is a bequest (wasiyyah), and it is stipulated that it must be within one-third of the estate. It is not enforceable beyond that unless the heirs approve. However, if the intention is to transfer ownership of the house to her during the parents' lifetime, then this is a valid and enforceable gift (hibah), and the guardian is permitted to take possession of it on behalf of the orphan.