The connection between the Vere name and the tree of the vampyre and werewolves may have come from the evolution of the word, “var.”
Of course the Vere name is tied to many royal and noble lines, as are the human lines of the vampyre and werewolves so there is a connection but not of the tree.
One line that is likely closer to being actually of the tree is the MacAlpine, as that root is alp (elf). Does that mean the human MacAlpines are supernatural or otherwise gifted? No, they are still human. It is simply acknowledging human lines that are, at some point, derived from the supernatural bloodlines. In fact, there are two MacAlpine lines. One is tied to the Picts (Merfolk) and the other to royal human lines. MacAlpines could be tied to both but it shows the blood distinction even in the human line.
The ties of the werewolves/vampyre to Djinn can also be found in the word var. The Djinn are said to be of the fire and var also means fire.
Several other related terms share the Var root.
And in my story, a certain comic Kangaroo is actually a Loup Garou and Tank Girl, well…