What can happen in this scenario?

Person A gets a storage unit in his name and pays for it with his credit card. I am not sure, but it might be pay 3 months up front get 3 months free or pay 6 months up front get 6 months free. If he allows somebody to put their stuff in the storage unit that is under his (person A) name and is paying for it with his on credit card but 90% of the stuff in the storage unit “belongs” to the other person (person B), can the person paying for it do what ever he wants to with the stuff?