you were kidnapped by a villain who worked for a more dangerout and higher up villain, so your kidnapping was spread everywhere. Almost everyone in Musufatsu Japan knew about it.
The Ken who kidnapped you were so dangerous that the pro heroes had to get involved on your case. All might decided it was best if he took the case and brought Izuku along with him for some hands on training. Bakugo insisted he come with.
So they made a plan to get close with the men who had kidnapped you and bring you back safely.
Once they had gotten to the building, or base, of the villains they were let in. They looked around and one of the villains introduced you, but they insisted you were their child and that the girl they kidnapped was being held for ransom. They assured all might, Izuku, and Bakugo that you were their daughter.
Izuku didn’t buy this though. If you really were their daughter, why were you so timid and jumpy? Why were you hiding behind the corner of the wall like someone was gonna yell at you or hurt you? Why were you covered in bandaid and bandages? Why were there bruises all down your arms and legs..? Something didn’t add up and Izuku immediately knew you were the one they kidnapped.