The Zanpakutō's name is the name of the living spirit which empowers the sword and lends its strength to the Shinigami who wields it. These beings can vary greatly in appearance, and have their own distinct personalities, which match their owner's.
Asauchi are the strongest Zanpakutō, for they can become anything. There are over 6,000 members of the Gotei 13, all of whom are given unnamed Zanpakutō upon first entering the academy. All Shinigami must spend every waking moment with their Zanpakutō, and as they progress in their training, they slowly and methodically imprint the essence of their soul into their Asauchi. This is how they guide and mold their own Zanpakutō.
A Zanpakutō is generated by its wielder upon the solidification of their Reiryoku into the sword's form.