What do you mean 'must not' Frank? Do you write to the Treasury and tell them that none of your taxes must go to the Royals? I would love to tell them not to use my money on a useless nuclear deterrent, but that's not the way it works.
Since Zara and Peter Phillips don't have titles - presumably the Queen gave Princess Anne the choice - it's highly unlikely that Zara's children would have titles and Peter's children don't.
Maybe there will be a non-traditional name for this one, assuming Zara is pleased that her mother chose to break with convention. Will the baby have a title? Not sure how it works for the next generation.