No. Actually your rivals default name is green. This is because FR/LG is a remake of the original Japanese Red and Green games where your rival should be Green and not on the International Blue and Red where your rival should be blue. So because of this your rival is Green and your player is Red. Source: http://bulbapedia.bulbagarden.net/wiki/Pokémon_FireRed_and_LeafGreen_Versions
