According to the Natinoal ITIS Standard Report Page, the Latin or scientific name for the domesticated cat is Felis catus. The word "Felis" refers to the genus and the species is Felis catus.
Cats can be described even more in-depth by Latin classification. For instance, cats are a member of the kingdom Animalia, the subkingdom Bilateria and the infrakingdon Deuterostomia. The domestic cat is also a member of the phylum Chordata, the subphylum Vertebrata and the infraphylum Gnathostomata. Finally, cats are members of the Latin superclass Tetrapoda, the class Mammalia, the subclass Theria, the infraclass Eutheria, the order Carnivora and the suborder Feliformia. This puts cats and all of their relatives in the family Felidae.