'non-isomorphism' is formed in English by prefixing 'non-' to 'isomorphism'; 'isomorphism' itself comes from New Latin/modern scientific coinage from Greek elements 'isos' meaning 'equal' and 'morphe' meaning 'form'.

'isomorphism' derives from Greek 'isos' + 'morphe', passed into New Latin/Neo-Greek scientific usage (e.g. 'isomorphismus' in German and 'isomorphisme' in French) and entered English as 'isomorphism'; the negative prefix 'non-' (from Latin 'non') was later attached in English to form 'non-isomorphism'.

Originally built from roots meaning 'equal form', 'isomorphism' came to denote structural equivalence in mathematics; 'non-isomorphism' therefore evolved to denote the absence of that equivalence.