There are a few universes that I want to list here and describe in more detail as well as provide more examples of how universes are named.
I use Elminster as an example, I claim no rights to Forgotten Realms created by Ed Greenwood. Many gamers know of the Forgotten Realms, so this is merely an illustration. If requested, I will take down this post and rework this example with Abraham Lincoln. It's just that I like D&D and this was the first thing that came to mind. Elminster's unique and detailed history lends itself to a full description of the naming system.
Forgotten Realms as an Example
3 Elminster IV - This universe is the Forgotten Realms in 1357 DR. This is the Forgotten Realms at the end of its 1st edition run before the gods were forced to the mortal world. The year is determined by when, in his world, Elminster was discovered by the Compendium. Using pithanoton particles, this was the fourth version of Elminster encountered. The time of the discovery of Elminster is set as a reference point to talk about dimensions four and five more easily.
Referencing events in the past or future of the Forgotten Realms would be 4 Elminster IV. The change from 3 to 4 represents a change in time. Time is relative, so there is no set time. Researchers may add a detail like 4 Elminster IV in DR 1385 (This would represent the beginning of the Spellplague.) or 4 Elminster IV in -2207 DR to represent a time during the golden age of Netheril. Both are 4 Elminster IV because it is a different point in time than 1357 DR.
Referencing alternate events of that world would be 5 Elminster IV. This would include a universe where the Blue Age lasted longer because Dendar didn't eat the sun or the events of the Spellplague never happened. For clarity, all fifth dimensional universe names include references to a year and at least one point of divergence from its third dimensional parent. Fifth dimensional universes are uniquely identified by their pithanoton signature. More on those below.
Everything has a pithanoton signature that helps Compendium researchers determine the dimensional origin of a specific person, place, or thing. It is also used to distinguish between two or more identical objects and to determine possible relationships between two or more objects. Specifically, this would help determine the difference between Elminster I and Elminster IV. Elminster I belongs to a universe that was created in a slightly different way than Elminster IV. In the Sycarion Continuum, Elminster I's world was created similar to our world, the creation mythology is different, and magic doesn't exist. The Compendium encountered this Elminster as a mathematician and theoretical physicist working in a particle accelerator facility. References to this world would be 3 Elminster I (which is around 2017 CE), 4 Elminster I (any time outside of 2017CE), or 5 Elminster I (an alternate reality where Elminster becomes an English teacher).
Remember that this system is about identifying universes, not individuals. As such, there is a 3 Dendar I where Elminster exists, but he is not the Elminster of any other universe. He has a unique pithanoton signature. The universe is named Dendar because he was the first object from that dimension encountered. Researchers do not trace every individual throughout the multiverse, even the most interesting ones.
There can be mistakes like the false discovery of 3 Elmara I. Elmara was encountered by the researcher, but the pithanoton signature quickly determined that Elminster and Elmara were the same person and that she was in an already discovered universe. Since this was around 232 DR, 3 Elmara I was reclassified as 4 Elminster IV, since it was a different relative time of 3 Elminster IV.
I don't plan to post anything about Forgotten Realms, it's not my world. I hope this serves as a helpful reference that is a bit more fun that using a former president.
Universes that I Will Write About
3 ? ?? XIV - Over 120 iterations of Lu Yùn Sh? have made contact with the Compendium. In this universe, metahumans emerged during their American Civil War. Metahumans feature prominently in their 19th, 20th, and 21st centuries. Other notable events are the rise of the Axum nation, a substance called Ball Iron, and 19th century planetary exploration.
3 Mordenkainen V - This is the universe of 5th edition D&D rules as written.
3 Ommtala IV is the universe of my family's fifth edition D&D game. It is also where Arethusa Atticus, the awakened dolphin psionic paladin lives. He is a character played by our beloved stuffed toy dolphin.
3 Sanderson II is the real world as we experience it. If I talk about real life, it will be tagged with this as a sort of in-house joke.
5 Sanderson II is the world where the narrator (the in-fiction author of all the posts) lived before working for and moving to 10 Compendium I
1 Inanitas I - This universe is also known as Solitude. Universes in the first dimension are either occupied by a singular being or an inert non-living point of matter. Some tourists visit dimensions like Solitude to find the ultimate sensory deprivation chamber only to discover a cacophony of noise and energy from other tourists. Others visit to discover the ultimate private chat room where nothing exists save for the visitors that meet there and an imperceptible point of unknown matter.
1 Omnis I consists of a singular point perceived as a line. There are an infinite number of 1 Omnis dimensions, but they differ only in the sequence of thoughts of their repetitive sole entities. The Compendium considers this odd effect of perceiving a point as a line to be the origin of the phrase "line of thinking".
Employing protective energy or magic has created a cottage industry for tourists to listen to the thoughts of a creature that has no known capacity to conceive of anything outside of itself. Many in the Compendium consider these tourists as extreme voyeurs.
2 Lotus XVII - This is the dimension that is home to Lotus. Sixteen other iterations of Lotus have made contact, but only this one maintains contact with the Compendium and other dimensions. Hailing from an advanced civilization, Lotus discovered pithanotons to allow travel to outer dimensions. Discovering magic in their travels, they travel by magical means.
Lotus is insatiably curious and enjoys sharing what they know. They hope to make contact with entities in 1 Omnis dimensions. They are the foremost authority on multidimensional travel. They possess a keen mind able to think in dimensions that they cannot perceive naturally. Lotus loves chess and ranks with an estimated ELO of 3600.
6 Phlisihu I - This is the home world of the celestial being, Phlisihu. Specifically, he is a Corrupter, a group of being that appear to enjoy antagonizing creatures in other universes. His favorite targets are elite magic users. He currently resides on a moon in 3 Ommtala IV where he is antagonizing Galen, a salt mage.
There are other universes still awaiting classification, but those will be detailed in other posts. If you made it this far, congratulations. More to come that is actual content, not blah, blah, blah explanation of how things are named.