'stain' originates from Old English, specifically the word 'stǣn' / 'stain', where Proto-Germanic '*stainaz' meant 'stone' (and by extension a spot or mark).

'stain' changed from Old English and related Old Norse forms (for example Old Norse 'steina'/'staina') into Middle English 'stain'/'steyn' and eventually became the modern English word 'stain'.

Initially it referred to a spot or mark (with roots linked to 'stone'), and over time it retained that literal sense while also gaining metaphorical senses such as a blemish on reputation.