We don't have synonyms for puter yet — it may be a rare, specialized, newly coined, or misspelled word. The closest thesaurus entries we have are outer, putter and pater.
(n) :
(childish, Internet slang, often endearing) Clipping of computer [(now rare, chiefly historical) A person employed to perform computations; one who computes.]
(n) :
(childish, Internet slang, often endearing) Clipping of computer [(now rare, chiefly historical) A person employed to perform computations; one who computes.]