"I'm completely exhausted," the actress admitted to Violet Grey. "I thought my wild nights were over, but these are some of the wildest nights I've ever had."
For now, Eva and her boyfriend Ryan Gosling are taking on the responsibilities of parenting by themselves, but the Place Beyond the Pines star is open to the idea of having a nanny in the future.
"Esmeralda has two amazing grandmothers and incredible aunties who come over and really help me," she said. "But as far as a nanny or a night nurse, for me that part of being a mother at this early stage is the struggle of not being able to sleep and not knowing what I'm doing and really going through it with her and battling out those nights."
Eva said although she's "constantly" worried she's going to do something wrong, she never hesitates to turn to the baby's grandmothers or aunties if she needs advice...or check out a particular site for moms.
"I try not to Google too many things because it is frightening, but I do go to babycenter.com and read the comment sections from other mothers because I find so much solace in that," she continued. "Just knowing that I'm not alone out there and that other moms have gone through the same thing can at least get me through the night."
As for why they named their baby girl Esmeralda Amada, Eva said, "we both love the Esmeralda character from the Victor Hugo novel The Hunchback of Notre Dame and just think it's a beautiful name. Her middle is Amada, which was my grandmother's name. It means "beloved" in Spanish."
The 40-year-old star also dished on her decision to stay out of the spotlight while she was pregnant, given that she and Ryan never confirmed to the media that they were expecting.
"Whether we like it or not, privacy is going to be very difficult for Esmeralda," she explained. "I think it's unfair but that's our reality. So Ryan and I decided early on to give her as much privacy as we could. And my pregnancy was the first opportunity to give her that."
"It's such an intimate time for the mother, too. I know that it seems all very innocuous when you're flipping through a tabloid at the doctor's office or see a photo of a pregnant lady online, but I find the media's "bump watch" obsession to be both intrusive and stressful. So I made a decision to eject myself from it completely. I was like, "Annnnd I'm out."