Stay The Same
These include the Lord of the Isles, Duke of Rothesay, Duke of Cornwall, Earl of Chester, Earl of Carrick, Baron of Renfrew, and Great Stewart of Scotland. Charles might have received most of his titles while Elizabeth was the Queen of the UK, but this does not apply to all of them.
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Changing Titles
For example, the title the Prince of Wales has been in effect ever since 1301. However, this does not automatically go to all heirs. As a matter of fact, this is a title that is reserved only for the male heir apparent.