NCC-640 is presumably the registry of the U.S.S. Copernicus, seen as starship filler in Spacedock at the end of STIV. When the model was reused as the Tsiolkovsky for "The Naked Now," the old registry was not removed, but the dedication plaque that Okuda made for the ship gave NCC-53911 as the ship's registry.
For TNG-R, the establishing shot of the Tsiolkovsky was shown to have the 640 registry digitally replaced by the newer 53911 registry. However, it appears that this was not done for the scene where the ship is destroyed. Most likely it was an oversight by the restoration team. So 53911 should still be the "canon" registry of the Tsiolkovsky.
On a side note (and I'm sure Mike Okuda can clarify this), I would suspect that when the dedication plaque was made, the Tsiolkovsky NCC-53911 was envisioned as a much newer ship design, contemporaneous with the Enterprise-D, since both ships were commissioned in the same year according to the plaque's stardate. Which would have also meant that the "Oberth" class was not originally meant to be the Grissom-type ship, and was only retroactively made so when the decision was made in post-production to reuse the Grissom/Copernicus instead of building a new model for the Tsiolkovsky.
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