Drampa appears to be based on a Chinese dragon, such as the Zhulong (torch dragon), a mythological creature with the face of an old man and the body of a dragon. Its friendly and caring disposition towards children, elderly appearance, and name may be a reference to grandparents.
Drampa may be a combination of dragon and grampa (a variation on grandpa).
Jijilong may be a combination of 爺 jijī (informal term for old man) and 龍 Lóng (Chinese dragon).