Of the Legends, Stein is the only one who's encountered Eobard Thawne before. While he doesn't recognize his true face, he probably would recognize him when wearing the Reverse-Flash suit as he does in the climax... except Stein is not present during this scene, due to helping Mick at the time.
Stein not being present keeps him from alerting Thawne to his destiny on The Flash (2014).
