Nope. Since she is married (and took her husband's name) her name (if someone wants to use a last name is Kate Mountbatten-Windsor. However, as a PP mentioned, titled British royals, officially, have no surname.
Wrong on the first part too. The change has to go through, not just the British Parliament, but, likely, Parliaments on the Commonwealth countries (it is possible that some countries don't require this, but I know that Canada requires a unanimous vote from all provinces for changes to the King/Queen). At this point, they aren't even sure exactly which bits of legislation would need to be changed. Our Prime Minister (and, I believe, all other Commonwealth PMs) have agreed, in principle, to the change.