Sure they can, but most folks just want them to be reasonable in their enforcement. For instance, if I send friends and family down without me, I could show them that they ARE indeed listed on my
MDE as friends/family and we also often travel together. None of them share my last name, as I have no living relatives with my last name. Even my now deceased half brother legally changed his last name after our father died, which is why I couldn't locate him while he was alive, I only foiund out after I did a DNA test on Ancestry, and it put me in touch with a first cousin on my fathers side. Not a hard and fast rule of, say, 10 reservations of one or two night reservations in a year, no matter the circumstances.