Inubou Kumichou is the father of Inuzuka Kouhei and leader of the Inubou group. He loves his son but views him as weak in regards to fighting and isn't comptent enough for the gang world. He had no idea his spoiled son was abusing his status as the son of a Yakuza boss to hurt others.
According to Ryuichiro Kuroda, he succeded the previous leader and was said to be as compassionate as his previous leader. Inubou Kumichou has never met Kumiko but has heard of her and respects her greatly as the granddaughter of Ryuichiro. He recieved a great surprise by her visit and more when she informed him of Kouhei's behavior.
This angered him greatly, as he had no idea his son was abusing his position in the group. Though he knows "I didn't know" wasn't excuse to Kumiko, he quickly apologizes. He then states that Kouhei takes after his mother and that he wasn't strong enough for the gang world. Thus why he won't leave him as his successor.
Though he wanted to severly punish his son. Kumiko talks him out of it and instead suggests the best way for him is to learn the hard way. So when he tries to contact them, he deliberately ignores his son's calls. Thus teaching him that he wouldn't have his father's status to fall on anymore.
His name is never really revealed. It is possible that his last name is also Inuzuka, but its never been stated.