And what if there are two thresholds?
With this, sir, you're on to something. And why stop at just two?
Just call it “threshold” and insert it after ability name.
Or "Trigger", and lose the ability name entirely - it's not necessary.
Example:
Keening Wail (threshold: 60 HP) The Troll sobs in despair over the state of its favorite roleplaying game. Creatures within 60’ who can hear must make a DC 10 Wisdom save and on a failure roll their eyes so hard they become Blind until the end of their next turn.
“Threshold” probably isn’t the best term, but something that denotes a numerical cut-off, not a physical state of the creature.
I'd far rather stick with fractions or %-ages to keep it simpler for DMs who want to tweak monster h.p. totals (a common 5e variant, I believe, sees DMs cut everyone's h.p. by half) and also to allow for similar creatures with somewhat variable h.p. totals as if those totals had been rolled. It would also have to be made clear somehow that triggers can only happen once per combat, otherwise regenerating or self-curing creatures might get broken fast as they repeatedly passed through a trigger point.
But, for your Troll it might look like:
Trigger 1 = 50% hit points: the Troll screams in pain and frustration. Anyone in the room (or within 60' if area larger) that can hear must make a DC 10 Con save or have no reactions, no bonus actions, no spellcasting, and -2 to hit and damage until the Troll's next turn.
Trigger 2 = 25% hit points: the Troll ceases attacking and seeks only to escape, immediately (regardless of turn order) fleeing in what to it appears the safest direction, bullrushing anyone who would try to stop it. If fleeing is impossible e.g. the combat is taking place in a closed room then the Troll will instead become mindlessly berserk for three rounds, gaining double its usual number of attacks each at +4 damage though during this time all to-hit rolls against it are at advantage.
Trigger 3 = 0 hit points: if a foe is within reach, the Troll gains an extra full attack sequence as it collapses.
And this multi-trigger idea can go into some class- or species-specific feats or abilities as well. Hobbits might gain +1 on their Con saves for each 10% hit points lost, for example; or a Rogue's sneak attack damage might suffer a progressive penalty for each 20% hit points lost - that sort of thing.
The more I think about it, the more wide-open design space I find here.