It is unclear what the registry or designation of this ship was intended to be. The nacelle pylons both prominently feature the number 4. Port nacelle features 4-CLN and the starboard nacelle features 444. On the top of the saucer section it reads B-24-CLN. The model was sold in the Propworx auction. The website of the auction features photos of the ship from varoius angles. 
The model used for B-24-CLN was one of the concept USS Enterprise study models designed by Ken Adam and Ralph McQuarrie for Star Trek: Planet of the Titans. Although the designations were not legible on screen in "Unification I", they appear on the study model, a photo of which was first made public in The Art of Star Trek, page 56.