I thought it was a given that Edward would get the title since he is the only one who is an earl. Charles is already Duke of Cornwall.
Once it reverts to the crown which can only happen once both Philip and The Queen pass away. Then Charles will issue LPs making Edward Duke of Edinburgh. The LPs for Philip’s creation (1947) have the standard wording “heir male lawfully begotten” which means it operates like any regular peerage and therefore Philip’s eldest son was always his heir and succeeded him to his titles.
I don’t expect Charles to use “Duke of Edinburgh” but he is now The Duke of Edinburgh...well The Duke of Cornwall, Rothesay, and Edinburgh if you wanted to get technical.
Personally this is probably a good thing. It’s very likely that the title won’t be used for 5 years (give or take) so there won’t be such raw emotion when it reverts to the crown and Edward is made Duke. A little down time will be a good thing.