| The Infanta of Castile story is itself the folk etymology in this case. It is believed Elephant and Castle is actually named after an elephant. In India an elephant has a howdah on it, the cabin arrangement in which you sit while riding it. This became known to the Crusaders, but the image was converted by heraldic artists at home into a castle, or to be more exact a tower. In heraldry when an entire elephant is depicted it is almost always an "elephant and castle".
Like any heraldic bearing, it could be used on signs to indicate ownership or overlordship. So pubs get to be called Elephant and Castle because that's the inn sign. There was one such at the place in London, which now gets its name from it.
In this case, the pub was founded in about 1760, on the site of a smithy used by the Cutlers' Company. This also used the sign. Cutlers make knives and knives have ivory handles: this may be why the motif was used.
British royalty has two connexions with Castile, the first being Eleanor of Castile (mar. 1254, d. 1290), queen to Edward I, who however was centuries before the term infanta was used; and an infanta who was once engaged to Charles I. She did not however set foot in England, as far as I know. | 
