Writers not associated with the hotel, such as those for The New York Times, very often use a single hyphen when referring to the Park Avenue hotel, sometimes not. Seldom do they seem to use "=", perhaps because they would then, to be strictly correct, put the registered trademark symbol after it, which is a pain in the neck. Or should that be pain-in-the-neck?
This does seem like a farce after all. Maybe a different choice of hotel chain is in order, so as to avoid the confusion.