Speaking to Latina magazine, Eva explained how she and Ryan settled on the adorable moniker, which means "loved" in Spanish and is a traditional family name.
"My grandmother's name is Amada, and Esmeralda Amada is the name of our oldest," said Eva. "We had a few names picked out for our new baby, and when she was born, we didn't feel like those names were her."
Eva Mendes welcomed her second child Amada in April
The Hitch star added: "We came up with a few more, even that morning, and tried them out. We were like, 'What about Viviana?' But we just kept going back to Amada.
"It was an emotional time with the passing of my brother. We thought how beautiful to go with what made us emotional and with what felt like her. When we looked at her, we thought, 'Aww, Amadita.'"
Eva had to explain to her Canadian boyfriend Ryan that their daughters sharing the same name wouldn't be that unusual. "In true Latin fashion, we reuse names all the time," she said. "I actually told [Ryan], 'This is common in Latin culture, so it wouldn't be crazy.'"
The actress lost her brother Carlos just days before giving birth
The actress' brothers are similarly called Carlos and Carlo. Carlos sadly passed away before he had the chance to meet his niece baby Amada, who was born in the same week that Carlos' funeral was held.
"We had a funeral service for [Carlos], and that same week, I had the baby. It was really, really intense and obviously beyond heartbreaking, but also kind of beautiful," said Eva.
Eva had to explain to Ryan that reusing names is "common in Latin culture"
But the 42-year-old admitted that she hasn't had time to process her brother's death. Instead she has been focusing on her newborn baby, and adjusting to her role as a mum-of-two.
"My older little girl is not yet two years old," said Eva. "My little one is still an infant, and right now it's really about surviving those nights and trying to enjoy this time as much as possible with them, and start the bond between Esmeralda and Amada. It's a really, really special time. I'm loving it."