Yes! He’s a hero in his own right, let’s have him adventuring under his own name!
But to answer your question:
It’s a bit complicated but in summary the sword came into being in the recent legion of X and sons of X storyline. A while back Kurt had Magik’s soul sword hidden within his soul, removing it left a gap in the shape of a sword.
Nightcrawler, unbeknownst to him filled that gap with his hope, thus creating the ’hopesword’ which is apparently more powerful than standard magic swords. It was also hinted that Kurt has an affinity to magic here which is why he gels so well with magic items. Margali cursed Kurt and turned him into a monster in order to pull the hope sword from his body and use it for her own nefarious deeds.
But Kurt was cured of the curse and the sword was returned to him which he now can store within his body and use at will.