With the passing of Douglas McGuinness Dudgeon, his son Douglas Tavish McGuinness Dudgeon has inherited the title of Royal Duke of Edinburgh.
That's not how a 'royal' dukedom works. A royal duke is a prince who has been granted a dukedom. His son, also technically a prince, becomes duke on his death. Duke II's son is NOT a prince (assuming Dukes I & II are not King at any point), and will simply be Duke of Whatever upon his assumption of the title, like any other Duke. Also, The Duke of Edinburgh was until quite recently Prince Phillip, aka the Queen's husband. The title is now held by Prince Edward and sure as hell never would have gone to an illegitimate son as it's very clear that titles can only be handed down via legitimate heirs. Kings have very occasionally managed to make exceptions, but not usually even if they have dozens of illegitimate sons but no legitimate heirs
