Two or more objects (cards, permanents, spells, etc.) have the same name if they have at least one name in common, even if one or more of those objects have additional names. Central Elevator's ability lets you search your library for any Room card that doesn't share a name with a Room you control on the battlefield, checking only the names of unlocked doors. If a Room on the battlefield has no unlocked doors, it doesn't have either of its names.

Promising Stairs's ability counts names, not permanents. A Room with two unlocked doors has two names.