A woman who marries a regular Duke becomes Duchess upon marrying but I'm not sure that's the case with Royal Dukes. But the Queen will probably confer a title on Kate. Diana became Princess Diana of Wales, but since Charles is still Prince of Wales she Kate won't have that title.
I'm too American to view any of this as being appropriate in this day & age & I would resist any US money going to this nonsense. But if the English want their monarchs, they aren't hurting anyone, so be it.