If that name seems familiar ... it's because Eiza was one of the breakout stars of "Baby Driver," she's also starring in the upcoming "Godzilla vs. Kong" movie ... and she's been connected to some of the biggest names in Hollywood.
But, on Thursday night, she was with Thompson at A.O.C. restaurant in West Hollywood ... and sources at the spot tell us they had a private table in the back so they could be alone.
Klay will get back on the court Friday night -- when his Golden State Warriors take on the L.A. Clippers at Staples Center in Game 6 of their NBA playoff series.
As for Eiza, her upcoming "Godzilla vs. Kong" flick is already getting a TON of hype -- even though it isn't scheduled to come out until 2020.