If the booking form asks for first name and surname, then it means first name and surname. Not middle name and surname. Not preferred name and surname. Not nickname and surname.
Jeez, how hard can it be?
I am known to one and all by a diminutive of my first name. Even my parents have never called me the full version of the name. However my passport, driving licence etc. all have my full name on them. My signature consists of my first name in full, both middle initials and my surname. That is my name, end of story.
Either change your name by deed poll and change all your official documentation or just accept that your middle name is just that, a middle name. It's not your first name no matter how much you prefer it.