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 (A, B) ordinal indicating which of the several possible simultaneous branches this one is. Because doors duplicate, there are only two : by right-hand rule ('A' the door knob is on the right, 'B' 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. 

For short-hand, the closest city and year works. For example: Athens-179A : Byzantium+238B

The shortest version will be the TELL of the most recently opened door in this universe (since time marches forward, there should always be only one). 

In your example, 'Earth 1' is BasementJan2020-A, 'Earth 2' is AtticFeb2020-A, 'Earth 3' is AtticFeb2020-B, and 'Earth 4' is BasementJan2020-B (if I have the order right).