Re: "there's a transition period after March"
"Surely the Prince of Edinburgh wouldn't want to give his city back to the Scots?"
There isn't a title in the peerage named 'Prince of Edinburgh': you're probably thinking of the 'Duke of Edinburgh'. This title hasn't been enduring because it has mostly been bestowed upon people who are in line to the throne or whose descendants are in line to the throne: if the holder, or their descendants become the monarch then the title merges with the crown and ceases to exist. Thus, the title had to be (re) created, for a third time, before it could be bestowed upon Phillip, who is only the fourth person to hold the title.