'process-server' is a compound formed from the noun 'process' and the agent noun 'server'. 'process' originates from Latin, specifically the word 'processus', where 'pro-' meant 'forward' and 'cedere' meant 'to go'. 'server' originates from Latin, specifically the verb 'servire', where the root meant 'to serve'.

'process' came into English via Old French 'proces' (from Latin 'processus') and Middle English 'proces' before becoming modern English 'process'. 'server' derived from Old French 'servir' (from Latin 'servire'), entering Middle English as 'serven/serven' and later 'serve' with the agent form 'server'. The compound 'process-server' is a modern English formation combining these elements to denote one who serves legal process.

Initially, 'process' referred more generally to a 'going forth' or procedure and 'server' to 'one who serves'; over time in legal usage 'process' came to mean a formal legal writ or document, so 'process-server' evolved to mean specifically 'a person who delivers legal writs/documents'.