@IM__TRASH_ Tomura killed all living Shimura relatives by mistake. He was left on the streets, waiting for a hero to come to get him. They never did. All For One picked him up and illegally adopted him re-naming him Tomura Shigaraki, going Tenko All For One's own last name, theoretically making him All For One's adoptive son. however, there are theories that All for one is Hizashi Midoriya, Izuku Midoriya's father. If this were true, Tomura and Izuku would be adoptive brothers, however, they are more often portrayed as cousins which is inaccurate.
For Inko's hero name, think of something to do with floating, as her quirk is a weaker version of Ochaco Uraraka's quirk. If she were a hero, she would probably be more of an underground hero, relying on strategies and physical strength due to the weakness of her quirk, almost similar to Shota Aizawa, the underground hero is one of the only heroes to rely mainly on strength and strategy, instead of his quirk, as Shota's can severely damage his ability to see. Inko would probably only use her quirk if she definitely had to, allowing her to store up her quirk's strength over time.