'payor' is formed from the verb 'pay' plus the agent suffix '-or' (used to form nouns meaning 'one who does X'), modeled on legal/administrative usage in English.

'pay' comes from Old French 'paier' (also spelled 'payer'), which in turn comes from Latin 'pagare' meaning 'to pay'. The agent-forming suffix '-or' comes from Latin '-or, -oris' via Old French and English usage; 'payer' and 'payor' developed as alternative agent nouns, with 'payor' appearing in formal and legal contexts.

Originally from Latin 'pagare' meaning 'to pay, settle', the basic sense 'to give money in exchange or discharge an obligation' has been retained; 'payor' preserves the agent sense 'one who pays' and has acquired specialized legal/financial usages.