So I understand that the way to get a true name of a demon is to charm it, such as with Charm Monster unless you find an ancient scroll. My DM rules that you can't command it to tell you it's true name because it isn't charmed (seems this is controversial, with a ton of people on both sides and thus up to the DM; seems fun to me either way).
With Summon Greater Demon, say you summon that demon again later but it runs out of hp, it would go back to the abyss, letting you summon it again later. If you cast it before a long rest, it would have the hp it previously had when it despawned because it is the same demon if before a long rest as a creature. This makes it seem like the downside of summoning a demon you know the name of is that the hp may be depleted. Does this sound right?
I've seen some answers though say you cannot even summon a specific demon. This idea is supported by the wording in Infernal Calling, where it says you summon that devil if you have its talisman with no such similar wording in Summon Greater Demon. So if these spells are read in light of each other, it seems pretty ridiculous to have to use two spells to get one demons name for one casting of the spell (SGD and Charm Monster). Or maybe not to some DMs?
Also, with the variant rule for summoning another demon at a percentage chance by the demon type, is that for the player too, the DM only, or the discretion of the DM? Seems like if you wanted to call in a demon for mass destruction, the first command would be for it to call its friend too.
Last, it seems that SGD just attacks what is closest if you lose control, ostensibly reducing risk of using it if you are smart about placement. It seems like a lot of DMs ignore this and make up an anthropomorphized story of how it didn't like being controlled and will then beeline to the summoner. Is this correct? I'm relatively new to D&D, and a lot of these rules seem poorly explained and up to interpretation or based on previous editions I haven't played.