After he returned home to Bizen, Mitsurugi encountered a rather pathetic katana set behind a tag identifying it as 'Ichimonji'. While no respectable blacksmith would ever admit to creating such a weapon, Mitsurugi had come to the realization that the strength of one's weapon is just for show. A warrior's true strength comes from within.
Looking at the sorry excuse for a katana, Mitsurugi was reminded of a younger him, a hopelessly ambitious boy who was the son of a simple farmer, yet gave himself the name of 'Heishiro MItsurugi' as a sign of his conviction to become an elite samurai. "It's a worthless katana, but it suits my style..."
After purchasing the blade for next to nothing, Mitsurugi renamed the sword 'Muichimonji'.