'Freed from Crank-a-Kai:'"Thank you for freeing me. I'll go anywhere with you!"
Pittapatt is based on the youkai called the Bakezōri (also its Japanese name), born from an old straw sandal: along with the karakasa-obake, it's one of the most common tsukumogami (youkai born from old items). They come alive at night and frolic around the house, but aside from the scares they may cause they're actually fairly harmless.
Pittapatt's habit of synchronizing its steps with a human's references a different youkai, called Betobeto-san: nominally a formless creature, illustrations usually depict it with a white, round body and no features except for a large, toothy mouth and two legs clad in wooden clogs. Betobeto-san is named after the sound its shoes make as it follows humans around, matching their pace and getting closer and closer, making the pursued victim go mad from the anticipation. But if said victim simply steps to the side and says, "After you, Betobeto-san", the youkai will walk past them and leave them alone.
In northern Fukui, a similar creature which appears during sleet storms in winter is known as Bishagatsuku, the name coming from the "pisha pisha" sound its invisible feet make in the slush-filled streets.
"Pittapatt" is a corruption/shortening of pitter patter.
"Gastong" is a portmanteau of Gaston (a French name) and tong ("sandal").
Pittapatt's "random" nicknames in Yo-kai Watch 2 are: Dalton, Flipflop, Shoebert, and Patter.