have not used in the progressive tenses (to own or possess something): We have a house in London.
have got informal (to own or possess something): Mike has got a nice car.
own (to have something that legally belongs to you): I don’t own my TV. I rent it from a shop.
possess formal (to have or own something): The fire destroyed everything people possessed.
be in possession of (to have something that legally belongs to you): She is in possession of most of the land around here.
hold formal (to have, own, possess): She holds a US passport. Do you hold any shares in this company?
boast (to have something that is a source of pride): The hotel boasts a nice swimming pool.