Yanking names away from ships so that they can be applied on other ships is standard naval practice (and fighting navies in general are much less worried about renaming ships than superstitious civilians). A mighty battleship might be forced to donate her hallowed name to a newbuild when herself relegated to coastal patrol duties, say.
Did this happen to the Hood? There is less precedent for ripping the name from an existing ship for painting it on another already existing ship, but that exists, too. And "perpetuating a ship" by moving the name from a wreck to a sister ship is a classic: most prominently, the Spanish did that to their celebrated España (although chiefly because the surviving sister ship at that point had a politically unpalatable name).
Most of the Starfleet name and registry weirdness is but a pale shadow of the real world, and shouldn't raise too many eyebrows. And if something really bothers us, we can plead extra weirdness from, well, weird being Starfleet's business. The Yamato might never have carried that five-digit registry, except in a log file corrupted by the Iconian virus; Riker in an earlier adventure would be thoroughly acquainted with this sister ship and would use the E-suffixed registry as proof positive of her identity, while Picard in the latter adventure would not pay much attention to yet another annoying glitch.
And, hey, even if we insist on freeze-framing the explosion to read the numbers painted on the saucer (which don't match those on the computer file anyway), DSC now shows us starships can change pennant paint in a jiffy, the Discovery's USS changing to ISS quickly enough, but the ISS getting changed back to USS happening fantastically fast, too, and apparently quite automatically at that. Apparently, the Iconian bug just commandeered a few paintbots...
Timo Saloniemi