Just played the demo, and thoroughly enjoyed it. There isn't really anything to criticize at this point, so nothing but glowing words from me. One thing I do wish was possible, would be the option for the player to name the prince themselves, as well as their alias after their change. As a trans woman, stories like this can prove a great relief from struggles one may have in daily life, and while this story can very much still do that, it would do it even better if the player was able to give a custom name to the MC themselves. Being able to use their own chosen name, could be a big chance for people to sorta engage with their own name, especially if they're in the closet for whatever reason, and can't experience the joy of someone calling them by their true name so to speak in real life.
The story seems good so far as it is, and my recommendation really just comes down to me nitpicking at this point, but I feel like it's an option that would only make people enjoy the story even more than they already would. As a fanfic author though, I can understand the importance of names to the person writing their story, so don't feel pressured into making that change if the current names are important to you. It was purely and innocent suggestion that you have every right to turn down or ignore.