If the last name is "Morgan," then "The Morgans" simply announces that name. "The Morgans' " is something you might see on a welcome mat or on a placard on someone's house. It's possessive and shows that it's their house. "The Morgan's" is technically possible but will almost always be a mistake because when we generally don't put "the" beforehand when its singular.
– Sep 26 '19 at 02:43
It depends on what's being expressed. What is the sign describing? A family? Something owned by the family? Something owned by an individual named Morgan? A group of British sports cars?
– Jason BassfordSep 26 '19 at 03:23