I would think they'd do well to avoid geographically naming the team so as to not ostracise any fans - they've got a better chance to do it than the Dolphins did (their attempt was a bit of a farce given the QCup side...) - e.g., would a Wellington league fan support a "South Island" team? As a case study, it will be interesting to see if Auckland-based Wellington Phoenix fans remain loyal to the Phoenix or shift their allegiance to the new Auckland side.
I'd be thinking a "Southern" team, even if they're Christchurch-based and play majority of home games in the South Island. The other benefit of "Southern" (or similar) means that it doesn't directly conflict with "New Zealand Warriors" - as my vote would be that the Warriors do not change that element of their name.