"In the Muggle world 'Potter' is an occupational surname, meaning a man who creates pottery. The wizarding family of Potters descends from the twelfth-century wizard Linfred of Stinchcombe, a locally well-beloved and eccentric man, whose nickname, 'the Potterer', became corrupted in time to 'Potter'".
-- J K Rowling (WW)
The Potter family is a wizarding family from Godric’s Hollow in Devon, although the family originated in the small village of Stinchcombe in Gloucestershire (WW).
Notable members of the Potter family
Potter as a surname is usually derived from a family whose occupation was making drinking and storage vessels (Old English pott, from Latin pottus, meaning "drink or draught") (Internet Surname Database). While J K Rowling, in her essay on the Potter Family (WW), has specifically said that the name comes from the fact that an ancestor was an eccentric potterer, ie someone who "occupies oneself in a desultory but pleasant way" (from mid-17th century pote, meaning "to poke repeatedly, push or kick") (Oxford English Dictionary), it is not really a push to also see that the potion-maker in question was certainly involved with producing drinks or draughts.
From the Web
Writing by J K Rowling on WizardingWorld (Pottermore): The Potter Family
The Rowling Library, TRL Magazine Issue #49: The etymology of the Potter surname by Leandro Bensussan Lemme
MuggleNet: What Does the Sneak Peek of “Harry Potter and the Cursed Child” Reveal? by Mikaela Martin
LiveJournal: In Search of Potter Relatives by lunar_music
Harry Potter Wiki: Potter family