Previously, plaques had been hung from the gate reading "Awaiting the Bearers of Virtue" (taiken), and then, during the reign of Sho Sei (1527-1555), this was replaced with a plaque reading, simply, "Shuri". Consequently, the gate was previously known as Taikenmon, and then Shurimon, after those plaques displayed at that time.
Though the plaque at one time read "Shurimon" the keen observer sees that today it is "Shureimon" (with an 'e' in the name).