I doubt it.
Among the Queen's descendants there's already a Zara, Isla, Savannah; "Joy" doesn't mean anything unsuitable (not a dirty word or anything), H&M are not working royals, so i think they can call their daughter whatever they want.
I think they will choose an African-American girl name as first name (my personal guess is Aisha). The second name might well be something like Joy or Hope, which are also popular girl names in America.