Of course nobody owns a name, but to use the pet name of the Queen is hardly the same as you or I choosing a name for our child. Obviously it is going to be mentioned in news stories all around the globe, and it would certainly be expected that she would be consulted. It's a private pet name, very personal to her, if they had wanted to call her Elizabeth, Beth, Lizzie etc. that would be different.
Baffles me how people can't understand that being a Royal, and therefore in the public eye, means that they are not the same as Joe/Jane Bloggs!!!!