Terrian, Elevation, Latitude, Longitude
I'd recommend the T.E.L.L. (time, elevation, latitude, longitude -- popularized in 'Travellers') of when and where the split from the 'primary' timeline occurred, and an (ALeft, BRight) ordinal indicating which of the several possible simultaneous branches this one is. Because doors duplicate, there are only two : by right-hand rule ('A''Right' the door knob is on the right, 'B''Left' on the left) This coordinate is local. So, the next branch would be relative to the new timeline.
A fully-qualified world name starts with the earliest time, and continues appending TELL-suffixes up to the most recent leaf.
Shorthand for Convenience
For short-hand, the closest city and year works. For example: AthensApril179Right : Byzantium238Left
This can be simplified further if only one door was ever opened in Athens. In that case, AthensLeft or AthensRight is sufficient.
On the other extreme, if hundreds of doors have been opened in Berlin the name can offer the necessary detail (up to the limits of your ability to know when and where the door opened). Examples : Berlin1931April26-179A0135, 0136, 0137 -- in that case, it may be easier to shorthand the event everyone is going to : Byzantium+238BBerlinOlympics-0135
Simplest Form
The shortest version will be the TELL of the most recently opened door in this universe (since. Since time marches forward, there should always be only one) "most recently opened" door.
In your example, 'Earth 1' is BasementJan2020 :
- 'Earth 1' is BasementJan2020Right,
- 'Earth 2' is AtticFeb2020Right,
- 'Earth 3' is AtticFeb2020Left, and
- 'Earth 4' is BasementJan2020Left (if I have the order right).
Alt-A, 'Earth 2'names. I think this is AtticFeb2020your set-Aup :
- E1 :
- E1 (also called E2)
- E3
- E4
Uniqueness of Synonyms for the Same World
Because of the time and location component, 'Earth 3'MyHomeTownBasementJan2020Right is AtticFeb2020pretty unique in all of the multiverse. It doesn't matter that the proper short name, after opening the door in the attic in MyHomeTownAtticFeb2020Right -B- both names are highly unlikely to conflict with another in the multiverse.
Disambiguation
Let's say that both AtticFebruaryLeft and BasementJanuaryLeft both decide to go to the same neighbor's house and open a door. In the unlikely event that both of these timelines open a door so close to the same location that you can't measure a difference, and 'Earth 4' is BasementJan2020-B (if I haveso close to the order right)exact same time that you can't measure a difference.
Then two completely unrelated sets of NeighborsMarch2020 have been created. It's possible to disambiguate by prefixing the parent world :
AtticLeft-NeighborsMarch, or BasementLeft-NeighborsMarch