'backstroke' is a compound of English 'back' + 'stroke'; formed in modern English to name the swimming style made while lying on the back.

'back' comes from Old English 'bæc' meaning 'rear', and 'stroke' comes from Old English (and Germanic) roots meaning 'a blow or movement'; the compound 'backstroke' arose in English (19th century) to describe the specific swimming stroke and then produced forms like 'backstroking'.

Originally a literal combination referring to a 'stroke' made on the back, it developed into the fixed name for the swimming style and the verbal/gerund forms used to describe the action.