A while ago I made an edit to Kris' page calling them "Kris Dreemur" and it was undone because it wasn't directly stated anywhere in-game; they could've had Toriel's maiden name after the divorce. But...
I was replaying Chapter 3 and noticed this quiz near the beginning of the TV world:
(image from Shayy's playthrough as I was too lazy to go back and take a screenshot)
Does this confirm that Kris (and possibly by extension Asriel) still has/have the last name Dreemurr?