You have the right to post pictures. You also have the right to tape your business card on the cake board under the cake so that when they cut it they see your business name right there so they know you made the cake.
On the other hand, if the guy who’s saying he’ll tell people he made the cakes is going to bring a lot of business to you, you might want to make some kind of business arrangement with him. People sell cakes wholesale to restaurants all the time, so it might be worth more to your business to sell to him. Does he have a cake business or a restaurant or what?