Lopez, 42, explained how her 3-year-old twins with ex Marc Anthony got their fruity nicknames during an appearance on The Tonight Show With Jay Leno Monday.
"I have this beautiful necklace which was given to me at Christmas," Lopez added. "There are two coconuts and their initials on it."
As they work out the details of their divorce, Lopez and Anthony, 43, will continue to share custody of the twins. Max and Emme will turn 4 on February 22.