An AU where Stain and Aizawa are both hero killers.

One of them is going to find Izuku and offer to train him, by this point he wouldn't know they are hero killers.

Over time Izuku trusts them more and more, until he eventually sees them as parental figures, more so than his own mother.

While this is happening, Inko notices Izuku becoming more and more distant from her, but doesn't know how to fix the situation.

Eventually, Izuku runs away, without the knowledge of The Hero Killers or his Mom, so he just shows up at their warehouse and tells them what he did.

They attempt to turn him away at first, but Izuku refuses to go back to his mom. He loves her, but he can't stand being around her because she looks at him with pity and treats him like glass.

So they end up begrudgingly agreeing. Inko, however, is distraught and reports it to the police immediately, they don't take the case very seriously and end up closing it within three months of receiving it.

Izuku ends up with a new identity, Kozuke Kinzo. His "guardians" had a few favors from people that could alter his appearance slightly:

His eye and hair are now a magenta (his hair is also cut and styled differently), he no longer has freckles and instead has a beauty mark under his right eye.

This appearance isn't permanent but is instead tied to a gemstone that was made from a quirk, as long as he is wearing it he will look like his new identity and not Izuku Midoriya.
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When he does the entrance exam, the teachers aren't expecting a lot from him, because quirkless.

Then he kicks ass and gets third place in the physical exam and first in written.

He gets in and on the first day immediately gets in trouble for 'unheroic behavior'.

"There's no one way to be a hero, and if we are being technical about everything, then I'm here to be an anti-hero, I'm here to call out and beat the shit out of anyone who deserves it. I don't give a damn if they're a hero, a villain, or even a corupt civilian."
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So yeah this is Anti-hero Izuku who was raised by two hero killers.

The situation with his mom is gonna bring drama and angst