Most cats are named in one of two fasions. The first is obvious, and indicates the physical characteristics of the animal. This mostly applies to recent breeds. Other cats, especially the more prized, such as Burmese and Siamese, are named after the region in which they are believed, or were once believed, to have originated.
The Tabby cat is different, although in a bizarre way it falls under the first category.

Attabia was a district of Baghdad, capital of modern Iraq, named after medieval prince Attab. A cultural center, it was the home of Attabi, a distinctive striped silk pattern.

The French enjoyed Attabi under the name Tabis, and when it was exported from France to England, it became Tabby cloth.

The distinctive markings on the common Tabby cat resembled the patterns of Attabi to the extent that the cat was soon named after it. Not so much a matter of homeland or characteristics, then, but a result of coincidence, and the fact that the British feel the need to mangle everyone else's language.