As long as we are part of the Spanish World, our ruler's name probably is Juan Alfonso Carlos Víctor María de Borbón.
Our tabloids never say anything about the Corona de España. I found out this info about la Rey by myself:
# Juan Carlos has a legitimate claim to Emperor of the Romans (Kaisar Autokrator Ton Rhomaion).
# After Franco's death, Juan Carlos I immediately instituted democratic reforms, to the great displeasure of his military.
# He is related to all European dynasties.
# Juan Carlos is an amateur radio Operator and a keen Sailor. In 1972, he competed in the Dragon Class event at the Olympic Games.
# Though Juan Carlos speaks several languages (fluent French, Italian, Portuguese and Catalan) with his Queen he speaks English.
One paragraph really got to my attention, I paste it entirely:
Rey de España
King of Castile, King of León, King of Aragon, King of the Two Sicilies, King of Jerusalem, King of Navarre, King of Granada, King of Toledo, King of Valencia, King of Galicia, King of Sardinia, King of Cordoba, King of Corsica, King of Murcia, King of Jaen, King of Algeciras, King of the Canary Islands, King of the Philippine Islands, King of the Spanish East and West Indies and of the Islands and Mainland of the Ocean Sea, Archduke of Austria, Duke of Burgundy, Duke of Brabant, Duke of Milan, Duke of Athens and Neopatria, Count of Habsburg, Count of Flanders, Count of Tyrol, Count of Roussillon, Count of Barcelona, Lord of Biscay, Lord of Molina, General Captain of the Royal Armed Forces and its Supreme Commander, Sovereign Grand Master Of The Celebrated Order Of The Golden Fleece, Grand Master of the Royal & Distinguished Order of Charles III, Grand Master of the Royal Order of Isabelle, the Catholic, Grand Master of the Royal & Military Order of St. Hermenegildo, Grand Master of the Royal & Military Order of St. Fernando, Grand Master of the Order of Montesa, Grand Master of the Order of Alcántara, Grand Master of the Order of Calatrava, Grand Master of the Order of Santiago, Grand Master of the Order of Maria Luisa, Grand Master of other Military Orders...
But... for diplomatic reasons, Juan Carlos cannot claim the title he wants the most: the Sovereign of Gibraltar.
Here's his casualidad to get even with the British:
He may officially add Nueva York Ciudad to los demás que correspondan a la Corona (the others pertaining to the Crown).
Grand Duke of Nueva Ciudad
A.k.a. Kaisar Autokrator Ton Rhomaion
Besides that: a Honorary Member of the Sons of the American Revolution.
That's already official: 10 years ago, NYU opened the King Juan Carlos of Spain Center in the Judson Hall, his NYC residence.