The Man-ape's whose fur and name change in the cold.
The Yeti or "Abominable Snowman" - snow-dwelling cousin of Bigfoot.
The caprivore with piercing teeth threefold.
Chupacabra - literally means something like "goat-sucker" and leaves three teeth marks when sucking blood from animals.
My adopted kin, for my only true brothers are gone.
They melted to black before history's dawn.
I think this must be referring to prehistoric creatures, such as dinosaurs, going extinct and becoming petroleum and coal.
Ask my name and I'll sing of my home.
I'm not sure but could be the Sirens..?
For no toe have I, nor knee, nor glome.
Ghosts - non-corporeal entities.
With monstrous fame of a ghastly sort.
Scary monstros, like vampires and mummies, in movies (or hiding in the closet).
I'm a notorious false report.
UFOs - "swamp gas," etc...
You won't get in if a key's what you've got.
Look on the map. The white X marks the spot.
X-Files - title screen/logo has a white "X."
I suppose you're the paranormal.
[EDIT: After adding explanations for the fourth and fifth lines, I'm wondering whether the answer must be made more general - changed to the unknown.]
[EDIT: A couple of my line explanations might be dubious, still.]