Traditionally when commissioning a work one gets all rights to it. You've basically paid for it to be created for you. Work for hire.
But not everyone follows those rules, and it's always important to discuss the policy that will be followed BEFORE you pay your commission. You should know exactly what you are buying.
So in this case, it sounds like you and the artist had different assumptions about the art, and its produced a situation that is a bit of a bummer. I'd get my art and enjoy it, and look at the fact that others will see it as perhaps a way you made some other peoples lives more positive as a side effect, then proceed with clear negotiations in future commission negotiations.
Myriads