Instructions
Point to the "Mii Channel" from the main Wii channel menu and press "A."
Point to the Mii you wish to change the name of and press the "A" and "B" buttons on the controller simultaneously to pick up the Mii. Hold down the buttons to hold the Mii.
Drag the Mii avatar to the "Edit a Mii" option on the left side of the screen. Release the buttons. The Mii editing menu appears.
Point to "Quit" in the lower left corner of the screen and press "A." The Edit a Mii option will ask you to name your Mii avatar.
Type in the new name for the Mii using the onscreen keyboard.
Point to "OK" and press "A" to save your changes.