Instructions
Travel to Goldenrod City.
Enter the Name Rater's tent at the north end of the city, past the bridge. It's the yellow and purple tent on the left side of the road.
Speak to the man inside of the tent. Once he rates your Pokemon's name, you will be given the option to change it. Select "Yes." You can only change the name of the first Pokemon in your lineup -- to change other Pokemon's names, place them in the first slot of your lineup using the Pokemon menu and speak to the Name Rater again. You do not have to leave the tent to do this.
Enter a new name for the Pokemon. Select "OK" to save it.