When you unlock this door, search your library for a Room card that doesn't have the same name as a Room you control, reveal it, put it into your hand, then shuffle.
(You may cast either half. That door unlocks on the battlefield. As a sorcery, you may pay the mana cost of a locked door to unlock it.)
(20/09/2024)
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.
(20/09/2024)
Promising Stairs's ability counts names, not permanents. A Room with two unlocked doors has two names.
