Oookay... Apparently, the Blu-Ray reworking of "The Naked Now" gives us a new registry number for the Oberth
class model seen on screen there, one matching the five-digit number seen on said ship's dedication plaque. That is, the earlier three-digit number is now gone (from all but one overlooked scene).
However, it came as a surprise to me that the old pennant on the physical model, supposedly a remnant from its appearance as USS Copernicus
at spacedock in ST4:TVH, is not "NCC-623" as the Encyclopedia
would have us believe, but "NCC-640".
The TrekCore screencaps from ST4, fuzzy as they are, seem to show a number more resembling "623" than "640" IMHO... Was the model reworked for some reason between ST4 and the TNG appearance? Was it perhaps given a new name as well? Did the VFX people turn the model into "USS Tsiolkovski
NCC-640" when the prop people used that name but for some reason chose a different number?
Or has everybody been seeing things all the time and "623" never existed?
Have a look at the ST4 'caps, offer theories, whip out a surprise card...