The person who rents a room in your home is your 'lodger' or a 'tenant'. I take your point that 'landlord' sounds rather formal and old-fashioned, but that it what you are. Otherwise, you could call yourself the 'homeowner' in this relationship, or as Peachey suggests, say that you 'rent a room to xx'. Roommate would mean that you are actually sharing a room: this term is mainly used by students in dormitories in the US. You could say housemate or flatmate, both British terms, but this could be misleading because it might suggest an equal status. I've never heard anyone say 'homemate'.

Tenant. You are the landlord/landlady, and the person renting is your tenant.