I think of it more like Air Force One... any plane the president happens to be on is "Air Force One" for the time being.
I suppose you make a decent point, though I hate to think of deleting old unused ships. I'm too much of a collector for that. I guess we're all so attached to the concept of our "Enterprise" that to have multiple ships under multiple names seems....wrong, somehow.
That said, believe it or not, you have swayed me. Each of my ships, going forward, will have a different name and registration than the last. Kudos, Rrellkhen, as you may in fact be the first person ever to have won an argument on the internet.
Lucky me, I already decided on four different names.
I'm perhaps a little strange but in my own private little Star Trek universe there is this little squadron consisting of four ships. The main ship is called Sanctuary and it's actually a modified Constellation class - whenever I get the chance to use a ship more fitting to my dream, I will just rename my old ship until I get a Constellation.
That way, I'll still be captaining the Sanctuary and get the chance to build my own little squadron ob similar named ships.
It wouldn't be fitting to have several ships named the Sanctuary flying around federation space. And if I ever see a Sanctaury I will bribe that captain to rename his ship.