It's not suddenly a significantly more capable road for that small crossover, it's not part of the Princes Highway, and shoudn't be tagged based off of it. 

For naming it, you can just go with noname=yes to indicate that section doesn't actually have a name.

If one were different, I'd say dealer's choice, but personally would go with the higher of the two. Putting it as the same as the road it's crossing just doesn't make sense to me.