Do you know what gender the second rabbit is?
A second cage would probably be a good idea, since the first rabbit is male.
Two adult males usually don't share a cage peacefully unless they're neutered (since we don't know their ages, I don't know how long you would have before this happens)...
I'm going to guess he's not a purebred anything, because that combination of size and color doesn't quite match any variety of any breed I can think of.
My (former) meat rabbits also did fine with just pellets.
(Although I have no objection if someone wants to provide 24/7 hay for their pet rabbits-- at the very least, it keeps the owner from worrying that their rabbit is hungry and "needs" more pellets than it ought to have.)
Rex rabbits have extra-short fur (feels like velvet.) That rabbit appears to have normal length fur, so not a rex.
I can also rule out:
Any kind of lop would have ears that flop, which this rabbit does not.
Any kind of angora would have long wool, instead of the normal-length fur I see in the...