What if Kris is basically just Frisk but restyled?
So just that after the events of the pacifist route, Frisk just renamed themselves to Kris because they didn't like the name and it's uncommon.
Since Frisk didn't want people to still call them Frisk, they changed their appearance entirely, and made themselves known as Kris. They took inspiration from Chara.
This theory is probably the most messed up that I have ever made, I made this because I was bored.
It’s pretty possible that they’re versions of the same individual but either way Deltarune obviously doesn’t take place in the world of Undertale and this should be very apparent by now