[Nyororin]

Is it possible that she is married and is listing head of household for the address? That would be something quite normal...

A daughter inviting someone for a homestay also would NOT be something all that odd, really, if the parents approved.

I don`t see any reason for there to be deception going on - Why list a male name if they were trying to trick someone into thinking they were female. Even if the person you`ve spoken to all along is a man, it`s probably more likely just a picture of a family member in front of the house rather than any active attempt at deception.