He was also a Prince of Denmark*, but renounced that along with his Greek title just before his marriage. And of course, he also converted from Greek Orthodox to (surprise surprise!) C of E!
* One can note echoes of his Greek and Danish background in his Arms as D of E. Will try and be clever enough to post an image....
Edited to add:
Success! Top left is Denmark, top right is Greece, bottom left is Mountbatten and bottom right is Edinburgh.
Interestingly (sic!), in the grant of those arms in 1949 he is referred to as
Sir Philip Mountbatten, so he must have already picked up his KG and/or KCVO by then....
...... really really must get out more......