Is this a low level, mid or high level campaign, does the sword have a purpose, special ability(s), or intelligence. Does the sword have a history/lore? Did any specific race or races forge the sword, if so, possibly naming as you would appropriately of that race <ie. elven>. Was this sword passed down through the family or found on the corpse of a_random_mob?
When making specific weapons/items for longer campaigns I like to ask myself many of those questions and put some real thought into it. Many people here have offered great suggestions for names for your sword. The final touches are up to you and how far you want to get yourself and said paladin into this. The sky is the limit. The more you put into the experience, the more your players will get out of it.
Try a name like 'Ever Vigilant', just an opinion...