Well, the shaking absolutely continues. But where Sans's answers and comments help distract Papyrus from the idea that he's freezing, the first step draws his attention back to his body. He staggers with the motion, but leans a little more into his brother's shoulder as he starts a very shuffling stride to keep up.

"I still can't believe... you named the sock."

To his mind right now, it's the most sensible explanation. One of the two inanimate fixtures of their old house traveled with them, somehow, across wherever they've come to - and the pet rock didn't transform into a human, the way they did. But if anything else were to haunt their lives, it would surely be that sock. What better to name the fake son of the photos around Sans's new house, than after it?