The name Rena is a girl's name of Hebrew, Greek, Russian origin meaning "joyous melody". Rena and is often added to lists like Names That Mean Happy and discussed in our forums with posts like "Girls Makeover - Two Middles".
From the experts:
Rena is a Hebrew name all on its own but may also be an abbreviation of Irene or an name that ends in rena or rene or reen. Also spelled RINA.