At the moment it's just "the Eglu". I used up all my creativity naming the birds! (Cordelia, Eris, Franziska, Faraday, Skaði, and Terezi. I am a huge nerd.)
Although... I did get the purple cube. Maybe once the chickens start laying I'll call it "The Eggplant", if Boondock Saint and chickerdoodle don't mind me stealing the name.
Okay, it's official, we're going with Maison d'oeufs! Literally Egg Home. I love it! I'm going to plant french lavender around and have red accents. Woohoo.