What is name of the red eyed rabbit or hare, found in Himalayan region?
Perhaps a bit underwhelmingly, those are Himalayan Rabbits.
https://en.wikipedia.org/wiki/Himalayan_rabbit

The pure white fur and red eyes are usually a sign of albinos, but in this case it's actually a trait of the entire species.


  [They] can only produce eumelanin under a certain temperature and they cannot produce pheomelanin at all.