Grandfather is never explicitly given a name in either the anime or the manga. He never seen in person; only appearing in dreams and flashbacks.
Prior to the start of the series, he takes care of Yuuri and Chito. He is also the one who provides the two with their Kettenkrad and tells them to go on their journey to the top levels of the city.
In extra chapter 2, it is seen that Chito and Yuuri have no recollection of their parents and are not related. Their earliest memory of any family is of their grandfather. It is unclear if the grandfather is actually related to either of the two.
Not much is known about his personality. The only thing that has been depicted in both the anima and manga was that he was very caring towards Yuuri and Chito.