Prince Charles is known as “HRH The Duke of Rothesay” in Scotland – since, as I understand it, that is his senior Scottish title as is traditional for the heir apparent to the Scottish throne.

Then is Prince William properly known in Scotland as “HRH Earl of Carrick”, that being Prince Charles’ next-highest Scottish title, as a courtesy title?

(If so, then presumably Prince William’s heir would be logically entitled to “HRH Lord Renfrew” if Charles had not yet ascended...)