Hey everyone,

if one of my companios is killed because I've sided with the "wrong" faction (or something like this) ... will his Perk still be activ?

Or will I lose the Perk with my companion?

Yes, the perk is permanent once you get it.

I also confirm this, I still have the Institute's companion's perk, although his body has been long gone from the little memorial I had made for him inside an abandoned house.