Not only is this a great idea, but we already know that Toady supports it in some form.
# PowerGoal170, AS LONG AS THEY DON'T DO IT TOO OFTEN, (Future): With a foot atop the slain alligator, the barbarian warrior cries "I name you Dragon Sword!" at his raised blade.
I agree that this shouldn't make the weapon more powerful or whatever. It might make it more valuable, though.
In your average myth, weapons do not gain status, they're made with it. The legend belongs to the wielder, not the weapon unless the weapon's nature was critical to the event itself
I think we have plenty of examples to the contrary -- weapons can gain status because of deeds done with them, even if the weapon's nature was not crucial to those deeds.
Kusanagi was renamed "Grasscutter Sword" after being pressed into service as a lawnmower. In LOTR, we have Bilbo and Sting, and a host of other weapons that were given one name at their forging but another equally famous name by their victims.
Zulfiqar was named "Spinecleaver" after being used to cut someone in half. In Christian mythology, the
Holy Spear was just an ordinary spear that happened to get used for stabbing Jesus.