Are you playing Gen 4 (HGSS for DS) or Gen 2 (GSC for GBC or GS for 3DS VC)? I think the trades are different in the remakes than in the originals.
In-game traded pokemon generally come with nicknames, too. For instance, the Voltorb you can trade for in Olivine City in HGSS is nicknamed Billy, and the Machop you can trade for in Goldenrod Department Store is nicknamed Muscle.
I highly recommend trading for Muscle and using her against Whitney's normal type team. I would avoid trading a female Dragonair for some girl's Dodrio in Blackthorn City. Dragonair is much harder to obtain than Dodrio in HGSS, especially considering the addition of the Johto Safari Zone.
