I'd like to think that while Eridians do not name the celestial bodies in their system after mythological being, they have their own version of Hopscotch or Solarballs or whatever personification of their star system.
The following corresponds to my headcanon about the 40 Eridani system.
Unlike Sol, 40 Eridani A (an orange dwarf) didn't form alone. Instead it was born with its companions 40 Eridani B (initially a white main-sequence star of 1.8 solar mass) and 40 Eridani C (a red dwarf). The stars consider each other siblings and travelled through the galaxy together. They initially had quite some difficulty with their three body problem but eventually they figured out how to get along and settled with both A and C both orbiting B at respectively 232 AU and 13 AU.
The trio experienced a tragic event 122 billion years ago - B started turning into a red giant and eventually as a white dwarf. Before its super destructive death, B and C along with a few planets who are willing to sacrifice themselves managed to throw the celestial bodies in their binary system to A, with A retreating away to 418AU.
While A was able to capture most of the planets B and C threw at it, most of them still ended up destroyed colliding with planets in A's system or accidentally gravitationally sling-shooting each other out of the system. A was able to protect its inner solar system where 40 Eri A b and 40 Eri A c resides, but its outer system was almost completely re-done.
Once a white dwarf, B fell into an eternal dormancy. While A moved away to better take care of its planets and the planets B left behind. C chose to stay close and watch B sleep.
If this is an Eridian equivalent of solarballs: While still grieving over the loss of B and their previous planets, the stars of 40 Eridani have a much better mental state than slb Sol lol. 40 Eri A is older than Sol, having a quieter magnetic field and less disruptive solar activities in reality. It also has more experience dealing with familial conflicts and understands the feeling of being overpowered by a loved one's gravity. And its sibling star C (and previously B as well) are always there to offer a fresh pair of eyes (?) if it ever has conflicts with its planets.
40 Eri A b, or Erid: The closest planet and friend of A. It is one of the only two original A-planets. It gained a beautiful ring during the mass collision era caused by B's death, which caused it a great extinction event but it still has life on it! Erid is one of the few planets in A's system who has memories of B and past planets.
40 Eri A c, or Twoworld: The other original A-planet who survived, though not fully as it lost most of its mantle and almost all its atmosphere during the great collision era. It lost a lot of its memory as a result and is still recovering, thus sleeping a lot. Erid and A take turns watching it sleep.
40 Eri A d (Threeworld) and 40 Eri A e (Fourworld) used to be two different planets orbiting A, who collided with each other due to their orbits being disturbed by B's death, and eventually formed a binary planet system. They don't really remember what happened before their birth but A and Erid were both open to talk about it. Their orbit is right on the brim of being ustable.
Threeworld was thrilled when it found out that its thin atmosphere is sustaining life (astrophage) and pointed out that its astrophage isn't of lower priority than Erid's lives when Erid asked it to move a further away orbit to permanently freeze its atmosphere and stop the doubling of astrophage. However, it later changed its mind and agreed to risk moving its orbit if Eridian life are really to go extinct. To its delight, Eridians were able to solve the problem on their own and even gifted it with a new species!
40 Eri A x, or 24world (40-world in Eridian and base-6 system), or "Grace" is the result of a gas giant from B's system colliding with an ice giant from A's system. It is overall a new entity and only has very vague recollection of its past. Upon confirming its origin, Eridians nicknamed the planet after their deceased alien savior Grace, who is also someone launched away by their dying home world and ended up settled in their system. Due to its complicated origin, x is on a very unstable retrograde orbit.
40 Eri C b, a small planet with a mainly CO2 atmosphere who were sent to the B-C system by A after B's death, as A doesn't want its sibling to be alone. Among all of A's planets, x is the only one who has met it.
40 Eri A has a total of 26 "planets". The number is largely a result of Eridians considering all gravitationally rounded non-star objects "planet", so a lot of celestial bodies that would be classified as moon or dwarf planets are also considered planets in the Eridian system. The lower number is a result of A having less materials than Sol due to competing with its siblings and a lot of the planets being destroyed or launched into outer space during B's death.
A mainly blames itself for the collisions of the planets and is learning to accept their deaths as part of life. It doesn't blame its own or B's planets for colliding into each other as it was a tragically chaotic scenario and the planets were the ones who died, and it very much appreciates and adores the planets born from the collisions.
A is rather concerned with x's retrograde orbit though, as it is both a danger to the other planets and itself. However A understands that x is extremely young and needs time to figure things out before settling to a stable orbit, and hasty changes might cause more dangerous than its current orbit. The planets collaborate to accommodate x's orbit.
Millions of years later, x would decide to become a rogue planet after developing an interest in the panspermia theory Grace and Rocky developed. 40 Eri A would respect its decision but be concerned that there won't be a star to watch it sleep. However, a few small planets (40 Eri A q, k, w - whose properties I haven't decided) who are also interested in exploring the universe would volunteer to become x's moon, and they watched each other sleep on their journey. x's plan is to first visit the solar system and meet Earth, then head towards Tau Ceti to meet the planet Adrian.
It's worth noting that while x would still have its rings when it leaves the system and would likely still have most of it when it reaches the Solar System, Erid's rings would have faded by then due to its proximity to its star plus not having shepherd moons to keep them in shape.
Now if 40 Eri A x is to meet the solarballs
40 Eridani A x: đľI am known as 40 Eridani A x by humans on Earth, previously the 24th planet of 40 Eridani A. I was formed from the collision in which the late gas giant 40 Eridani B x swallowed the late ice giant 40 Eridani A 'h'. I'm mostly made of (insert elemetns) and I used to orbit 40 Eridani A retrogradely at angle of 160° on an orbit with an average radius of...đľ
Earth: excuse me we only asked for your name
40 Eridani A x: That is my full name!
Uranus: My name is Uranus... Please don't make fun of my name.
40 Eridani A x: đľI certainly wouldn't!đľ
40 Eridani A x: đľUh, apologies in advance, what is the difference between anus and mouth, question? You all have audible mouth, why ashamed, question?đľ
200+ moons in the Solar System: *introduces themselves*
40 Eridani A x: đľ*easily remembers all their names and greets them back*đľ
Jupiterian and Saturnian moons: *stares at their gas giants judgmentally*
Earth: I'm a rocky planet
40 Eridani A x: đľOh hi I'm a grace planet!!!đľ *proudly raises sphere*
Planet X: I was ejected against my will :(
40 Eridani A x: đľHuman Grace from Earth who used to live on my oldest cousin 40 Eridani A b was ejected against his will too. Why Solarian sentient beings eject members against their wills so often, question?đľ
(TBH I haven't watched much of Solarballs and actually doodled the Eridianballs as an Eridian equivalent of Hopscotch's personified singing planets. Though after gaining some context about solarballs I start to think it'd be interesting if the Eridianballs are to meet the Solarballs lol, largely because I imagined their star system to be a lot more wholesome, with much less hierarchy.)
Eridianballs... biology and sociology?
Solarballs have faces like humans and has a very much English-speaking Earth culture. Eridianballs, however, are personified in an Eridian way. Instead of faces they have 5 limbs that can sometimes disappear into them if they want to appear with a spherical shape. They communicate like Eridians through some sort of magical sound waves that somehow travels through vacuum because Solarballs can apparently also do that.
Their culture is also largely Eridian and puts a focus on looking out for each other and watching each other sleep. Stars don't sleep until they use up their fuel and become a white dwarf / neutron star / black hole. Planets do, so stars watch planets sleep. Their social life is also much less hierarchical and much more... communal - solarballs are hierarchical because we humans gave celestial bodies a rather hierarchical classification and somewhat considered planets to be more important than dwarf planets and than moons, but Eridians just don't have that concept.
