Is it permissible to transfer a government-provided housing unit to the daughter's name after her assignment to a government agency, given that there are other applications for housing, and that the nature of her work might require her to examine men?

If the administrative housing system does not prevent transferring the housing unit in your sister, the doctor's, name, then there is no objection to it, provided that it does not lead to infringing upon the rights of others. However, if it involves bribery, then the prohibition becomes even more emphatic and severe.