To rename these two party members to the name of your choice, within 4 character limits. First save your game and reset. Resume the Dragon Warrior 2 game, then enter the "continue/New Game/Option" menu. Choose "continue" to where it shows your log files. Place the arrow next to the log file where you would like to change there names, and enter one of the following codes.
Prince of Cannock:
Hold:LEFT+SELECT+START and then press A.
The rename prompt should appear for him.
Princess of Moonbrooke:
Hold:RIGHT+SELECT+START and then press A.
The rename prompt should appear for her.