I don't know the answer to that question about her attending the funeral of George VI. It seems likely, if she went to events in the UK both before and after that funeral.

Personally, I like the story of her name, and how history follows the human figure - meaning, it all began in Spain with a noble lady called Eugenia de Montijo, who goes to France and becomes Empress of the French when she marries Napoleon III. Then Q. Victoria and husband visit Paris for the Exposition there, and perhaps a friendship begins at that point - or at least, Eugenie feels safe and welcomed to the UK when the Second Empire collapses. And perhaps Q. Victoria's daughter was reminded of this background of relationships when she named her daughter Victoria Eugenia. But, that might be just my speculation..