Eva, 40, gave birth at the beginning of September but both her and 33-year-old Ryan have remained very private about their baby girl.
But US gossip website TMZ have now reported that her name is Esmerelda Amada.
Eva’s Cuban heritage obviously played a big part in the name choosing, as Esmerelda means ‘emerald’ in Spanish.
The name is also said to have been inspired by actress Eva's 2007 part in film We Own The Night, in which she played a character called Amada.
Not only have Ryan and Eva given their daughter an unusual name, but other US reports claim the new mum has an adorable nick name for her.
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She is said to call her 'Preciosa', which means precious in Spanish.
Unsurprisingly the couple are 'besotted' with their little girl, and a source said: "Eva's in the deliriously tired but blissfully-in-love stage where she wants to do everything herself."
Meanwhile Eva's brother Juan Carlos has praised their parenting skills.
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He told InTouch magazine: "They're great parents.
"Ryan's going to he a great father. He's just such a down-to-earth, nice guy. You couldn't ask for anything better."
Evan and Ryan have been together since 2011, after meeting on the set of movie The Place Beyond The Pines.