'agate-adorned' originates from Modern English as a compound of the noun 'agate' and the past-participial adjective 'adorned'. 'Agate' ultimately traces back to Greek 'achátēs' via Latin and Old French; 'adorned' comes from Latin 'adornare' (to equip, decorate).

'agate' came into English from Old French/Latin forms ultimately from Greek 'achátēs' (named after the river Achates in Sicily); 'adorned' developed from Latin 'adornare' to Old French 'adorner' and Middle English 'adornen', yielding modern English 'adorn' and its past participle 'adorned'. The compound form is a straightforward modern English combination.

Initially it would have been understood literally as 'decorated with agate'; that literal sense has remained stable in modern usage, denoting objects bearing agate ornamentation.