The Weeping Ghost
I stumbled upon a Worth Point listing for a pre-Scream packaged Wall & Door Plaque. Fun World advertises all of their wall plaque characters on the back of the packaging, and there it was: the 'Weeping Ghost'!
This is the only official name we can confirm Fun World used for the character. Though many call it the 'Peanut-Eyed' ghost, this is the best evidence we have for the commercial title of the character.