The grandfather is never explicitly given a name in either the anime or the manga. He is never seen in the present, and only appears in the girls' dreams and flashbacks and has potentially passed away following Chito and Yuuri's departure from their home.
The grandfather appeared to be a well-educated man, with a large collection of books ranging from pre-war folk tales (such as a book about kappas) to historic records of war. He is literate and is presumed to have taught Chiito how to read the language used in their universe. It is not specified as to why Yuuri never learned to read from him.
Grandfather also knew how to drive, and mentions how he had taught Chiito to drive the Kettenkrad. Yuuri also knows how to drive the vehicle (although not very well), but it is not clear whether the grandfather had taught her also, or she had learned while traveling with Chiito.