"She was meant to be mine," gushed the 22-year-old actress, who plays the pixie-like vampire Alice Cullen in the popular series, of her new puppy, Marlow. "I wasn't looking for a dog, and I happened to see her picture online, and I was like, 'I have to have that dog.' "
The lucky canine in question – a white Toy Fox Terrier – spent the evening in the lap of luxury as Greene lovingly cradled her throughout much of the For Joseph launch party at the new Kitson Melrose in West Hollywood. The twosome even posed for photos with Greene's fellow on-screen vampire, Kellan Lutz – Marlow showing her excitement by alternating between dozing and shivering.
"I'm already so that girl that brings her puppy to an event," Greene admitted to PEOPLE, adding, "I just got her today, and I was like, 'I can't leave her home alone all day!' "
As for how Marlow got her name, Greene said, laughing, "I really liked the name Harlow, but that's Nicole Richie's kid's name, so I thought that might not be entirely appropriate, so I just changed the first letter."