How to write and abbreviate a "scientific name", under the Linnaean system, and according to the International Code of Zoological Nomenclature.
The species is Tyrannosaurus rex, where rex is the specific epitetus. Here is called species because it gives the species, but it does not designate a species itself (it is never written just rex whithout the genus).
*Complete species should include author and year, though.
Example extracted from "The Complete Dinosaur, Second Edition".
Additional info (avalaible in Wikipedia):
T. rex may also refer to:
Tachyoryctes rex, the king mole rat, a rodent species
Tetragonodon rex, a seed shrimp species native to the Mozambique Channel
Thoristella rex, a sea snail species endemic to New Zealand
Trialeurodes rex, a whitefly species
Tyrannasorus rex, a fossil beetle species from the Miocene
Tyrannobdella rex, a leech species
Tyrannoberingius rex, a fossil gastropod from Miocene Alaska