I didn't nickname very many of my Pokemon back in Gold/Crystal, but I may do it this time around, like I did in Platinum (in which I nicknamed every single one of my party Pokemon, my starter included). These are the names I've been thinking of for my HeartGold team:
Cyndaquil (F) - Hinoa, a shortened form of its Japanese name. The name even sounds female.
Mareep (M) - Volts. This is the name I gave a Mareep in Pokemon Mystery Dungeon 2.
Bellsprout (M) - Leif. Based off the word "Leaf", of course.
Heracross (M) - Dura. Short for "durable".
Lapras (F) - Haven't decided on a name for this one yet...
Teddiursa (M) - Bailey. No explanation for this one except that I was going to use this name in an RPG once.
I may replace one of these with Eevee - especially if I can't evolve Bellsprout until Kanto. xD If so, it'll be a female Eevee named Eris. This is similar to the name I gave my Espeon in Platinum, Aris.
I'll be doing something similar in SoulSilver if I buy it. I'll be using the male character, and most likely starting with Totodile (M). If I do this, I'll be naming it Wanino, a shortened form of its Japanese name.
As for the Gyarados... it's unlikely I'll be training it, but I may give it a nickname anyway. How about... Pyro?