I can't seem to find the answer for this anywhere, and it seems to be rather random.
Yesterday, I engaged the frost troll on my way to the greybeards (as level 7), and after 1-2 hit, my character made the finishing move on the troll, but my companion died. Since I wanted my companion, I reloaded the game, and then realised that the troll is level 22 and I couldn't really kill it (I died from 2 hits).
What happened the first time when the troll got a finisher? Is it random or is it triggered by something specific?

Random, when you have a finishing blow it might at random decide to show a finishing move, or not.

So the troll simply died normally? It's just weird, cause it was my first attempt ever, and I didn't even realise how strong it was, and in my next couple of attempts, I couldn't really get him further down than 90% =(

Yeah I believe so...

I think it has something to do with their stamina, It seems to happen when I shield bash them and they stumble, I get one almost every time.

I seem to trigger finishers more often when my killing blow is a power attack.

That's because you do more damage and thus are more likely to kill your opponent with that hit. It's nearly impossible to get a finishing move from a second swing that barely hit the opponent and only actually hit them (and thus killed them) because you either moved slightly to your right/left/forward or aimed just at the last second at the opponent. If you want a higher chance to get a finisher, look at your opponent all the time and attack one hit at a time. Not slashslashaslashslahs while dancing around.

Finishers are interesting. A coupleof things I`ve discovered about finishers..

1. Finishers seem to happen if the victim is very low in health and you do something like a critical or high damaage kill. It`s NOT based on the last person killed.

2. If in first person it will show the kill in 3rd sometimes, but about 40% it`ll show the kill in 1st person which I prefer.

3. there`s a slight randon element thrown in.

Hopefully, when Modders get the CK, they and maybe even I, will find out what figures this and make mods to suit certain tastes.