Oh, absolutely. That's why I included the rest of my post: most importantly, that it is a UK passport (it doesn't take an expert in titles to understand that in the UK, Prince is a title and not a name), and that everyone of course knew who the patients were. I don't believe that the person who filled out the birth certificate is kicking herself saying, "Oh, I think that nice red-headed English chap was named Prince."
I think we are kidding ourselves that, again particularly given that the Sussexes were evidently quite upset about what was done to their first child's birth certificate, somehow this one was filled out with information they did not approve or they consider incorrect because they handed over Harry's passport to someone who did not know how to translate the information to the form.