This is the earliest mention I can find of a “Jack Russell” Terrier. The man, himself, was still alive; he died in 1883.
From The Staffordshire Sentinel - June 9, 1879:
LOST, small, Broken-Haired "Jack Russell" Terrier BITCH PUPPY : white, with black mark over one eye. —Apply, Thomas Atkinson, at Minton, Hollins, and Co.'s, Stoke-upon-Trent.