Vintage Toy: The Squooshy Rubber Face Finger Puppet!
This is Steve's and I think I recall us calling it Mr. Gaglio.
There are four finger "tubes" on the back of this puppet's head that, with a little dexterity, allow you to twist this guy's face into all sorts of horrid expressions.
Okay, enough of that.
They come in at least four different faces. Here's a selection that was offered on ebay!