The logical thing to do, as we have had the Cooper S is to call it the Cooper T. That way BMW wouldn't need to use the 'Traveller' name in their marketing, but it would still be affectionally known as the 'Cooper Traveller' by its fans.
Although if they were to release a turbo version that would make it the Cooper ST and I'm not sure how that would sit with Ford's range of performance cars.
Alternatively how about the 'Mini
MO' (
MO as in Morris Oxford) as a nod towards the original Morris Traveller.