Oleanda, so do I. Her name is Catherine for a start. Whilst I accept that a diminutive of Catherine is Kate, I was always taught that you do not shorten anyone's name unless they introduce themselves by the shortened version. My neighbour is Catherine and I would never dream of calling her anything else (and happen to know that her family only ever call her that). Another neighbour is David, I would never call him "Dave".
Since she is always announced by her family as Catherine, Princess of Wales (etc), I assume she has decided to take her husband's titles and name. Consequently, she ought to be referred to by that name. Some people decide not to take their spouse's name and that is also OK - (I have a professional name and a married name and I have indicated I will answer to either, but that is my choice.) It's just sloppy journalism that has caught on.
Mind you, it was a long time before Sophie Rhys Jones was referred to as anything other than that; and Diana Spencer equally as long. Sarah Ferguson is another example.