I can only remember a few named weapons in games I've played in. I think this is mostly because of the way magic items are handled in D&D - they're part of the character, not really their own unique items. Sentient weapons are the only ones that seem to get names, IME.
The best, I think, was Judgment of the Sultan, the sentient vorpal sword someone found back in 2e. It was a scimitar, and used as an executioner's blade for an old sultanate. Unfortunately, it was also Lawful Evil, and corrupted the PC who ended up with it, eventually turning her into an assassin. My druid didn't really care, though, since the sword agreed with his politics. Everybody else seemed really concerned about it, though. ;-)
My current character, a githzerai ranger/psychic warrior, had a blade he called Redemption. It was a semi-sentient weapon he got from a githyanki, and had a fragment of his own personality put into it, rather than the (evil) personality it had before. Sort of like a psicrystal in that way, I suppose.
In a Planescape game, I remember a sword called Agony. It wasn't something I had, and I don't remember all the details, but I know it was described as a fragment of the Lady of Pain. Really powerful weapon, as I recall.