It's Falkor, REbek.

In response to Rebekkin's quest (slash denial), I respond with (although no question was asked) this:

Cute, lovable, mighty, flying Falkor. Apparently there is some debate about whether his name is spelled with a K or a C, though I found more spellings with the K, like on wiki. I know, the learning just abounds in this post. However, did I find any Balcors out there? Not so much. I got one of those Google remarks, "Did you mean: falkor neverending story" that so nicely pop up when you misspell or mistype a word. But Rebek, you are cute and lovable too.

Don't you also want to scratch behind his ear?