The tag doesn't necessarily need to be freed up, but like how the characters Red and Green are based on [Fire]Red (in [Leaf]Green, the player would be "Green" and the rival "Red"), the HGSS rival would likely take on the same structure, far as an accepted name would go. Assumably on my part, the rival's default in SoulSilver would be "Heart".
Kotone, when not chosen as the player character, is always Lyra.