I see a huge mistake people confuse form of government with royal house.
we must distinguish between the form of government of a state, monarchy or republic, and Royal House. The Royal House is not a form of government of state, It is a historical entity. If I say: "Pavlo of Greece" is correct because it is in his passport, if Isay "Crown prince " , it is correct also, because the Royal house is historical entity, the titles of nobility are for personal use, it belong to the person who carry it. The titles are not of the States. Pavlo of Greece or Crown Prince is personal election but a person can not require another who thinks the same as he. a person can not impose to others. The titles of nobility have a personal character and this is reflected in agreements and recognized in judicial decisions. THe Prince Pavlo is the Crown of Hellenic Royal House, it is one historic entity that part form of the historic of Greece, Today we could not speak of state of Greece if we don´t study the monarchy.In conclusion one person can say:- ex prince of Greece, based on the old form of government of the Greek state to 1974. - That same person can choose the name of the person's passport "Pavlo of Greece ". And thirdly, that person can choose is personal , Crown to the Hellenic Royal House and is valid because the Royal houses have one actually outside the state, are historical entities.
And Glücksburg is a serious mistake, because it is not in any document, not name, is a place, a title that does not belong to the Greek royal family, and it is not in their passport, and there are statements that recognize that it is not his surname.