Is it permissible to receive the full salary despite not completing the required working hours, given that the work is divided with the administration's knowledge and there isn't enough space for the doctors?

If the hospital director is authorized to distribute work and rotate doctors, there is no harm in that. Otherwise, it is not permissible to violate the terms of the contract. The same applies to overtime hours; it is not permissible to record them for someone who did not work them unless the director is authorized to permit that.