The League found out Dabi’s a Todoroki because while you two were being intemeite you moaned out his real name and for the next three hours he ravaged you so hard you saw stars and he made you keep saying his name until you've both finished at least three times. There's was no way the League didn't hear you yelling about how you belonged to Touya and praising how good he is to you while he was practically feral for you hearing you moaning his name.