“So why S&D had to come out with a new Uncle Moishy instead is calling him something else like Fred is beyond me. Unless the guy’s real name is Moshe, in which case they get a pass.”
Uncle Fred or Uncle Chaim doesn’t have the goodwill and name recognition by kids and their parents that the name Uncle Moishy has.
Whatever the artist’s real first name is, is not that important. He can choose to use a pen name or trade name when acting, that’s different than his personal name. Many do exactly that with great success.
A businessman who does business even under his full personal name can sell the rights to the name or business and then he no longer has the right to sell that service under his name. If Charles Schwab sells his brokerage firm, he cannot start a new brokerage firm under his name — since the new owners of Charles Schwab have the rights to the name and trademark.
These are all generic points; I have no idea what happened with the ownership or rights to the Uncle Moishy name and business. (And it is a business and trademark.)