What does Reina mean?
The Spanish word 'reina' means 'queen', descending from Latin 'regina'. Also spelled Reyna. (A separate Hebrew/Yiddish name Reina meaning 'pure' exists; the Spanish 'queen' sense is the relevant one here.)
What does Paloma mean?
The Spanish word for 'dove', from the Latin palumbes 'wood pigeon, dove'. It carries a Marian and Christian resonance (the dove as a symbol of the Holy Spirit and of peace) and appears in the title Virgen de la Paloma.