Pookie.
Star
…so that he could be Star T. rex
**King o’ the Fores’ **
…after the line in The Wizard of Oz (even though that rhymed with Brontosaurus
Reason or Reed or Stout
… for obvious reasons.
Tyrone
I happen to like “Happy.”
Of course the full name would be something like “Happy Decimus Toothgnasher, the first.” But you have to just go with the use-name.
We have Terrier owners, I don’t see the problem.
Stampy.
Sorry, the name “Fluffy” has already been given to a giant reptile.
Alternate suggestions: “Mr. T”, “Chaos”, “Cthulu”, “Fido” and “Steve”.
Anything except “late for dinner”.
Fido
Or, possibly
Tiddles.
Bowser.
Sweet Pea.
Hey, a T-Rex needs love, too. 
Rover, of course. It’s the traditional pet name, and therefore cleverer than any number of clever names.
Crichton or Spielberg would be good
Two pages of replies, and nobody has suggested Sue?
Tiger. It would add an element of irony, I think.
Peckerhead.
Caspar.
Twinkles.
Rosie O’Donnell.
I vote for Dittohead One and Two. If they’re twins, of course.
Wow, how did I miss that on the first pass…must have been the brilliance of the Ditka suggestion before it. My first thought was Dr. Phil, but Rosie just seemed funnier.
On review, I change my answer to Ann Coulter.
Tiny
(as in “Meet the Robinsons”).