Perhaps the Protostar was originally a ‘top secret’ ship? Section 31? In which case it would not have a dedication plaque as it would give too much information away.
Perhaps. But, I don't remember the USS Prometheus having a dedication plaque (or at least I don't recall one being shown on screen) and it was an NX class too (at least at the time) - although admittedly that doesn't mean much. Its possible that certain NX class ships just don't get dedication plaques because they are expected to be test platforms for new technologies that will be used in other ships (but if a vessel distinguishes itself while testing those technologies, then it may get a dedication plaque)... or it was a missed detail on behalf of the CGI team (it can happen). I wouldn't be surprised for the NCC version (Perhaps called the Protostar-A - the one we saw in the last episode being unveiled on SF Academy grounds) to have one though. It is also possible the Protostar's dedication plaque was elsewhere on the ship and was just out of view?
Even if PRO set designers forgot the dedication plaque... its not something to lose one's head over because its a minor mistake at best. Also, its possible it fell off when the ship was badly damaged after passing through that temporal anomaly initially (or the second time) or the Vau'N'A'Kat removed it (because they wanted to pilot the ship back to SF to infect and destroy it - and the civil war survivors who wanted to destroy SF would likely see the dedication plaque as a thorn in their eye). Remember how the Diviner was irked when he saw the SF delta commbadge on Gwyn in episode 9? Similarly there was a Klingon at the Denaxi spaceport (frozen planet) who doubled back when he saw the SF delta commbadge on 'esngin' Ascencia (there was a similar emphasis/focus on the delta much like we saw with the Diviner).
Right...because Trek fans are known for their levelheadedness in the face of minor mistakes and inconsistencies...
The Prometheus-class Prometheus had a d-plaque in the port side bridge turbolift alcove. The Excelsior-class Excelsior didn't have one in STIII, but had gained one by STVI by the time the Okudas and Sternbach had gotten ahold of the franchise tech continuity. The Excelsior had gone from NX- to NCC- in that time, though. Plus of course all bridge variants of the Defiant on DS9 had one except for the mirror universe version. For all we know though the plaque of the Protostar was elsewhere. On the Nebula-class Phoenix, it was in the ready room of all places. The bridge of the USS Sutherland had one too, though it's largely accepted that THAT set was the ship's battle bridge or auxiliary control room (or kitchen, as the set was partially constructed from the galley set of the Enterprise-A!). Mark