Penélope Cruz and Javier Bardem
08/03/2013 at 08:25 PM EDT
Have Penélope Cruz
and Javier Bardem finally decided on a name for their daughter
A week after welcoming their second child, the actor paid a visit to Madrid's central registrar office on Tuesday morning, where he reportedly registered the couple's baby girl, according to Spanish magazine Vanitatis
So what moniker made the final cut? If the reports are true, 2½-year-old Leonardo's little sister, who was born on July 22, is named Luna Encinas Cruz. Luna means moon while Encinas is Bardem's first surname.
Notoriously private when it comes to their personal lives, Cruz, 39, and Bardem, 44, never officially confirmed Luna's birth
Reps for the couple did not return PEOPLE's request for comment.