In Avengers: Endgame Pepper Potts dons the Rescue armor. Does it have an AI assistant? If yes, what is its name? We have seen Iron Man use J.A.R.V.I.S. and F.R.I.D.A.Y, and Spider-Man has Karen and E.D.I.T.H.
It would appear so, in Avengers: Endgame when Pepper goes to see Tony after his Snap she asks F.R.I.D.A.Y. to examine him. It isn't exactly clear where F.R.I.D.A.Y. is talking from as they both have their helmets off but it is presumably from the Rescue suit as Tony's was damaged from the Snap. You can watch that scene here.
F.R.I.D.A.Y.: Life functions critical.
The Rescue Armor also has the same HUD and advanced functionality of Tony's suits and even lets her know about the incoming flood so that she can alert Doctor Strange about it. It seems unlikely that Tony would add all of this functionality in but not an AI, in fact, some of it probably doesn't work without an AI.