What is the origin of Scooby-Doo's name?

Here is a video of Fred Silverman, CBS' head of daytime programming back in 1969, discussing the creation of Scooby-Doo. Starting at about 1:40, he describes hearing "Strangers in the Night" while on a plane and conceiving the Scooby-Doo name on the spot:

On the plane, I couldn't sleep -- y'know, it was a Red-Eye, and I'm listening to music -- and as we're landing, as we're going in for the landing, Frank Sinatra comes on, and I hear him say "Scooby-dooby-doo", and it's at that point I said, "Yeah, that's it! We'll take the dog, we'll call him Scooby-Doo, move him up front, and it'll be the dog show!"

So this is about as authoritative as you can get: Scooby-Doo's name was inspired by the Frank Sinatra song, and not the Kinks song. As you note in the question, and as others have noted in the comments, "scooby-dooby-doo" may not have been the actual lyric, but having been listening to it through tinny 1960s speakers, Silverman clearly misheard it.

Fred Silverman's explanation cited in F1Krazy's answer has always suffered from the fact - as noted in the comments - that Sinatra sings 'doo be doo be doo'.

(Frank, incidentally, reputedly described Strangers in the Night as 'the worst f*ing song I've ever heard' - but that's neither here nor there.)

Scoubidou is the name of a 1959 hit (in France) for Sacha Distel, who had to settle a copyright claim by Abel Meeropol, the songwriter of the original from which it had been adapted without permission.

(Something else that's neither here nor there, is that Meeropol was the adoptive father of the orphaned children of Julius and Ethel Rosenberg.)

It's not implausible that somebody wishing to avoid copyright problems might go to some effort to establish an alternative narrative.

This is, of course, entirely unsubstantiated.

As a boy, Scoobydo was a knotting craft fad. We'd make these squared off plaited things with colorful, flexible wires. Nice. With that in mind, I googled, and got "Scoubidou (Craftlace, scoobies) is a knotting craft, originally aimed at children. It originated in France, where it became a fad in the late 1950s and has remained popular. It is named after the 1958 song of the same name by the French singer Sacha Distel." So who knows? Dooby doo Sinatra style, mistakenly heard as Scooby doo and voila! A hound is born!