my new headcanon/story for RHxDoctor is that Derpy almost dies so the Doctor feels bad and erases her memory and leaves her so she's safe. Then later he meets RH, so this plot twist is irrelevant xD
discord:aww i could be her friend to love
The show team noticed this phenomenon and decided to keep her eyes that way and showing her on the later episodes with her walled eyes as a small shout-out to the bronies. The show team went as far as to give her a small speaking role on the second season but unfortunately she was considered offensive towards the disabled and they had to alter her by correcting her eyes and changing her voice.
TL;DR: She is called "Derpy" because of her derped eyes.
The song fits this pairing so well!♥♥♥