What is the name of the "squeek" when playing the guitar?

Basically, it is the unintentional sounds that are made by the fingers repositioning themselves on the strings when the player changes chords or notes.

Artificial and/or “pinch” harmonics make that squeal. It’s actually included in some musical notation.

Roy Clark never played with the squeak. I think it would be a lot easier to play guitar with a squeak than without it.

It depends as well on the texture/composition of the strings. A smooth string (like Nylon) would make little sound while a wrapped string (like steel) would be more apt to make noise.