ok so ik its confusing but heres what i think is happening:
people feel really bad for espers-- since theyre helping save humanity but are treated like trash. so the higher ups have decided to give espers training to fit into human society, and theyre paired with guides, or veterans, im not really sure.
micheal/eve was the first esper they genetically manufactured: remember the chapter with the backstory? about the demons that came down, destroyed earth, but got slayed by an angel on its dying breath? and scientist took genes from that angel and integrated them into humans, calling them espers? well, micheal was the first esper, and he was super duper strong and unstable. so they locked him up and created "children" with his genetic code, altered to stability. the first generation of children was eliminated, but this is kind of irrelevant to the plotline so far. puppy, the pretty pink haired one, is a part of the second generation, and all these "children" call michael their father.
now, since micheal was super strong, he could read and potentially manipulate guides he worked with, in this case, adam. so to prevent michael from manipulating anyone from the past and to almost reteach him to not do this, they erased his memories, and his memories only. every other esper seems to have theirs. once espers are reintegrated back into society, their guides rename them, and adam renames micheal after his dead cat, eve.
also, this wasnt made very clear, but it seems when the decision to retrain espers into society was passed on, adam decided not to take micheal in, leading for him to stay abandoned until he was the very last esper. no one would take him in because he was too strong for the guides to handle: adam seems to be one of the only guides strong enough to handle him.
uhh i think thats it.