Harvey (at least the one from the film) is a púca – more commonly spelled “pooka” – a shape-shifting creature from (mainly) Celtic folklore that may bode good or ill fortune. The name probably comes from the Old Norse term pook or puki, which means “nature spirit.”
As far as we can tell, this obscure mythical creature has appeared (in hare form, one of its more common manifestations) on film a total of three times; its two other rather more sinister incarnations being in Sexy Beast (Fox Searchlight Pictures, 2000) and Donnie Darko (Pandora Pictures/Newmarket Films, 2001); although pookas pop up frequently in literature in their made-to-order roles as demon familiars/imaginary friends: eg. the gentlemanly Fergus MacPhellimey in Flann O’Brien’s [born Brian O’Nolan] (1911–1966) At Swim-Two-Birds (Longman Green & Co., 1939), and Robin “Puck” Goodfellow in William Shakespeare’s (1564–1616) A Midsummer Night’s Dream (1595/96).
*Prog 2024 at 2000 AD Covers Uncovered