Remi, I don't fully understand your position.
By law and custom, kings and members of the royal family have a dynastic name, but no surname. Perhaps you are saying the distinction is academic, so we should ignore it. If that's your argument, I disagree but I can see why it might be attractive.
I got a good chuckle out of Erica's comment that we should look at Henry VIII's baptismal certificate. Her comment was certainly tongue in cheek, since Henry VIII is the one who ordered baptismal records to be kept. It's unlikely he had one himself.
We know enough about medieval baptismal customs to know that Henry, at his baptism, would have been named as Prince Henry, or Henry, Prince of England and France. In English law of his time, the surname could be changed, but the baptismal name could not. He would not have been baptized with the name Henry Tudor!
It gives me a little bit of grief to think of Henry VIII losing the closest thing he had to a surname (of England) and ending up with a surname that is not supported by contemporary sources. But, maybe that's easiest for genealogists. If that's what we're choosing, I'll go along.
I think similar logic would push for the surname Plantagenet for the descendants of Edward IV's father - since he was the first to use it as a surname. I don't like it - it's the same kind of confusion between surname and dynastic name - but I can see why it would be "easier".
I hope we'll be careful about applying the name Plantagenet to the whole dynasty. Wikipedia says,
"Since the 15th century, Plantagenet has been applied retrospectively to the descendants of Geoffrey of Anjou as their surname. There is barely[1] any contemporary evidence for the name before the mid fifteenth century, and the house itself used no surname until the legitimist claimant Richard Plantagenet, Duke of York, father of both Edward IV and Richard III, assumed the name about 1448."
The John Plant article cited by Wikipedia is very interesting. I used to have easy access to the Nomina journal, and always read every article with great interest. The Plant article is available in pdf format, from the Wikipedia link, if anyone is interested.
Large swathes of the medieval tree use an interesting convention for royal names. The territorial name (of England) goes in the surname field, and the dynastic name (Tudor) goes in the maiden name field. I don't know who came up with that idea. It looks odd when you're entering the data, but it displays very nicely and intuitively.