The bird makes a call that sounds like the word “dee”, over and over. Just as someone who runs is a runner, a bird that’s dees, is a dee-r, so it’s not deer in the sense of the animal the way you may think. At least that’s what I’ve been told. The “kill” part is a bit strange, but I’m assuming it comes from the fact that this bird will feign a broken wing to distract a predator away from their nest. All in all, I’m really not sure on the origin of the name, but that’s what I’ve learned in my last 3 years of actively being a part of the birding community.
I’m a birder. Lots of birds were named after people…Scott’s Oriole for example. You may think a guy named Scott discovered the bird, but nope, just a friend of the guy that did. Scott wasn’t a good guy according to history (re: killing native Americans), so there’s a big committee that’s going to rename a ton of birds that have eponymous names. The birding community is very split on the topic and it’s interesting to see the drama.