Never trust what you read on the Internet.
The trademark is for "Kewpie," but since it's not actually printed on the dolls (at least the ones I own), I suppose it wouldn't have taken long for people to start writing it as they heard it. We locals know the correct spelling because, well, it's local -- one of Port Allegany's few claims to fame. (Yes, the town name is misspelled on that link. As usual, I blame Smethport.)
Now, do you want to talk about Greggg or dolls?