He's a famous celebrity of Star City so even if persons don't know Oliver it's pretty damn implausible that more than 100 Star City citizens don't recognize Oliver Queen is Green Arrow after seeing Green Arrow.
It's obvious DC comics saw this huge hole that which requires persons to accept something implausible so they fixed it with giving him a hood that makes him a lot less exposed the hat that leaves most hair shown and domino mask has most of his face shown including the facial hair.