We don't know Eve's last name. Why? Because Enzo doesn't know it, and he's our only source of information.
Like Denny, we don't meet Eve until she's a fully-fledged and independent woman stumbling into Denny's apartment with love in her eyes and perfectly manicured nails—the likes of which make Enzo very jealous (6.1). This is Enzo's first experience sharing Denny, and it's the first time he gets a good glimpse at what human family life might be like. At first, he does not like it.
We would say Enzo has only child syndrome, but he was born in a litter, so who knows the real reason?
During the beginning of Eve's interactions with Enzo, the two avoid each other, dance around one another, and vie for dominance in Denny's affections. As Enzo says, "We were both satellites orbiting Denny's sun, grappling for gravitational supremacy" (4.6). Even during Eve's pregnancy, and after Zoë is born, Eve and Enzo have a slightly strained relationship. They get along, but he's not her dog—he's Denny's. And even though Eve is now a part of their lives, both Denny and Enzo seem to know that.
Can it be called a turf war if it takes place within one apartment?
Once Enzo offers an olive branch of friendship, though—which Eve rewards with belly rubs—they decide that they can get along, and their relationship begins to take off. Enzo knows that his own fear was keeping him from loving Eve, and once he understood that and embraced that there wasn't anything to be scared of that he couldn't control, their relationship starts to work.
It's a good thing it does, too, because as it turns out, Enzo provides a real comfort to Eve as her headaches and mood swings get worse. He acts as her security blanket when she can't articulate her pain to Denny, and he keeps her together when Denny is off racing. In fact, when Denny feels helplessly out of his element, he asks Enzo to take care of Eve for him, and that's what Enzo does: "I took care of her by curling up at her bedside, or, if she had collapsed on the floor, by curling up next to her there. Often, she would hold me close to her body, and when she did, she would tell me things about the pain" (12.10).
Enzo understands this pain and knows that while he can't help Eve, he can be there for her and keep her company as she works through it.
Therapist, security blanket, protector, free vacuum for kitchen floor crumbs—is there anything Enzo can't do?
The relationship between Enzo and Eve becomes even more important when Eve's illness develops further. Enzo acts as her saving grace, protecting her the first night she really has to come to terms with her illness. This is a defining moment in their relationship, and it shows how much Eve and Enzo have come to understand each other. She begs him, "Get me through tonight…That's all I need. Protect me. Don't let it happen tonight. Enzo, please. You're the only one who can help" (23.109).
Since Enzo has been with Eve through these bad times, especially when Denny has been away, it makes sense that he is the one she turns to now, when her fear and pain are so strong that words can't articulate them. And since Enzo is so tapped into the idea of an immortal soul, he seems like the perfect candidate to protect Eve's while she's going through this moment of self-doubt.
Enzo's help isn't enough to save Eve, of course. Maybe it all could have been avoided, in the end, if Eve had gone to the doctors earlier or if she had treated it differently, or hey, maybe if she had drunk boxed water instead of bottled. Partly, it was her decision. But we can't explain exactly why things turned out for her the way they did. Life has a funny way of dealing you a hand that you might not expect, but it's how you deal with it that makes a difference. This is life, and life-threatening illnesses aren't something to be glossed over or ignored.
Oh, look, a puppy!