Pompeo, 40, appears on Wednesday's The Ellen DeGeneres Show, where the two Ellens chatted about baby nurses and onesies.
But it seems Pompeo's husband, Chris Ivery, is equally invested in his daughter's appearance: "He loves dressing her up like him," Pompeo says. "He goes out and buys her clothes that look like his clothes."
Pompeo, meanwhile, loves the fact that she has an "amazing" baby nurse to help ease the challenges of new parenthood and her career. "I couldn't do it without her," Pompeo says.
DeGeneres also added a personal touch to Stella Luna's wardrobe: a onesie that says, "I Love Ellen."