Different game features can affect a target at the same time. But when two or more game features have the same name, only the effects of one of them—the most potent one—apply while the durations of the effects overlap. [...]
The Essentials Kit has a further clarification on these rules in its "Effects with the Same Name Don't Stack" section (page 3, emphasis mine):
[...] But when two or more effects have the same proper name, only one of them applies while the durations of the effects overlap (a duration is a time span of 1 round or more). [...]
I'm unsure whether the further clarification will change my following examples but we do know for sure that with overlapping identical effects, one instance will be what I'd call "active" (will have effects) and the other will be what I'd call "inactive" (won't have effects). That all squared away, I think my question will make more sense with examples:
The Fire Elemental's Fire Form trait:
[...] The first time it enters a creature's space on a turn, that creature takes 5 (1d10) fire damage and catches fire; until someone takes an action to douse the fire, the creature takes 5 (1d10) fire damage at the start of each of its turns.
If a creature is under the effects of multiple instances of Fire Form, and somebody uses their action to douse the fire, are both instances removed or only one?
The booming blade spell:
[...] If the target willingly moves before then, it immediately takes 1d8 thunder damage, and the spell ends. [...]
If a creature is under the effects of multiple instances of booming blade, and they move, are both instances removed or only one?
The hold monster spell:
[...] At the end of each of its turns, the target can make another Wisdom saving throw. On a success, the spell ends on the target. [...]
If a creature is under the effects of multiple instances of hold monster, and they succeed on a save, are both instances removed or only one?
Can an "inactive" effect end when its end-condition is met (letting them end simultaneously), or do these sorts of things always end one at a time? Or perhaps the answer is something in-between?
There is also the following related question:
Both answers there supports that if you are grappled by multiple creatures and you make a check to remove a grapple, you only remove one of the grapples. It's not perfectly analogous situation but it is somewhat similar.