Yes I believe all party Pokemon should have names besides their species name. Here are the nicknames of my pokemon. Empoleon: Perry Luxray: Diddy Loppuny:Thumper Gardevoir: Rose Floatzel: Barbra Pachirishu: Bree And My HeartGold Team Loppuny: Cream Gardevoir: Sarah Meganium: Cherry Ninetails: Miles Pigeot: Falco Ditto: Kirby Pokemon, Like People and Pets should have their own name. It would be silly Just to call a cat,cat.
Actually, I played the Japanese HG/SS versions long ago and beat them. I don't have the US versions... yet? Personally though, I'm doubting I'll be buying them. However, whenever I feel like though... I will play them as roms.