Nah, actually by Deku. The marks on his face are supposed to form an x like when Deku uses full cowl.
It’s not tattoos, it’s his power. Shadow power makes the user stronger through negative emotions, but if he uses too much, he’ll lose control and end up destroying everything, which other shadow users don’t really have a problem with (cuz they’re evil). The more he uses the power, the more bigger the marks get until it fully envelopes him (full shadow form).