No no no, you're doing it wrong. What you need to do is get a Tokay Gecko and name it "Gecko."
Then you have (order, infraorder, family, genus, species, subspecies, pet's name): Squamata Gekkota Gekkonidae Gekko gecko gecko Gecko.
My son named his three leo geckos; Luke, Leia and Wicket. Do you see a theme here?