A normal Pidove is forgetful. Forgetpato literally forgets everything that ever happened, unless the thing involved her evolutionary friend (NoWarQuill). Even if she does remember a NoWarQuill moment, she is bound to forget about it a moment later.
Forgetpato comes from "forget/forgetful" and "Mamepato" (Japanese name of Pidove).
Forgetpato takes Pidove's forgetfulness and levels it up to eleven (which in itself is a reference to TV Trope "Up to Eleven").