[cyberdemon]

here's a theory i have tell me what you think.

Spoiler for theory:

Moka wasn't born to Issa. She had another father. One who came from a family with a very special ability. The Shuuzen who were a part of FT knew of that power and needed it but knew he would never help FT so they had him killed and Issa adopted Akasha and Moka into the family without them knowing the truth of what he did to manipulate them for his own gain.

Unfortunately Akasha wasn't raising Moka to the ideals of the Shuuzen family so they sent Akuha there to deal with the situation. Eventually Akuha kills Akasha and Moka happens to see. The two of them get into a massive fight that no one wanted to happen again.

Moka is then given the rosario which Akasha had modified to seal off her father's side of the blood which had something the Shuuzen family wanted so that they wouldn't be able to get. By sealing that half of her blood, Moka was only left with her mother's half which is why sealed up Moka looks exactly like her mother.

The Shuuzen family found that they were unable to remove the seal by themselves so they simply left Moka to do whatever she wanted which was why she was living in the human world up until going to the youkai academy while using her real father's name since the Shuuzen family saw her as useless then and didn't want her using theirs.