What name? "Speedy", "Artemis", or (with Roy's costume) continuing "Arsenal"?
I'm thinking that she modifies the costume, and probably goes by "Artemis", since it's more dignified than "Speedy". Plus, with Oliver's having been publicly pegged as The Arrow twice now, Team Arrow might not want to take the chance that someone who knows them recognizes "Speedy" as Thea's nickname, and puts two and two together.
Of course, I've overlooked the possibility of a different name. But "Speedy" and "Artemis" are the two that I've seen talked about the most.