I think you did. You tamed him, didn't you? Tamed animals don't trigger traps, but animals -with a name they got because they killed something and before they were tamed- will never stop killing your dwarves. So you either have to knock him unconscious on a cage trap to trap him, or kill him.
He hasn't even caught the critter in the first place, how could he tame it?
Also, the named critters being untamable is the result of dwarves/wardogs/etc. it hurt while wild remembering his hostile status and attacking, with the animal defending itself. If the critter hasn't harmed your dwarves or their animals, there should be no hazard to taming named creatures.
If he's trap-immune, you could try and build an enclosure of two tiles, two doors, and 8 constructed walls, like so;
╔══╗
┼^^┼
╚══╝
One cage trap, one single upright wooden spike trap. The idea being you poke him with the spike every now and then in the hope you'll do
just enough damage that he falls unconscious while on the trap.
Alternatively:
Z+1
......
.++O..
▼+..+.
......
.++++.
......
Z+0, ground level
++++++
++++++
▲╔##╗+
+┼^^┼+
+╚══╝+
++++++
++++++
You build the wall with grates in the middle, build a ramp up, then a floor section above the corner, and another left of that, and finally a constructed wall. Both traps in the enclosure are cage traps. Then, once the critter is trapped inside the enclosure, deconstruct the second floor, dropping the constructed wall(setup insures the dwarf won't be standing on a part that will collapse if you do it right) - this should kick up dust that can knock dwarves, and hopefully animals, unconscious, and as your critter only has cage traps to stand on...
...or just lure him into an enclosure and leave him there with locked doors.