What does Regis mean?
From Latin 'regis', the genitive of 'rex' — literally 'of the king', i.e. royal/kingly. Popularized partly via Saint Jean-Francois Regis. Means 'of/belonging to the king' rather than 'king' itself.
What does Aurelius mean?
Roman family name from Latin 'aureus' ('golden'), ultimately from 'aurum' (gold). Borne by the emperor Marcus Aurelius; a literal 'golden' meaning.