In Vietnam names like Nguyen Thi Anh Mai are common.
The family name is "Nguyen" is the family name. "Anh Mai" is the "first name". But they should be called "Mai". And reversing the order "Mai Anh Thi Nguyen" is just wrong.
And Catholic families in Vietnam often have names "Nguyen Thi To but everybody calls me by my baptismal name of Mary". Or you have a "house name" (i.e. your real name) and an outside name (so that ghosts can't follow you home). Or you have your real name and an unofficial English name (for reasons both good & bad) that literally everyone at work calls you.
In the Philippines people have names Anna Katrina Gomez. But you don't call them Anna. You call them Katrina because that's how it often works in the Philippines.
The solution is simple:
One field is "what is your full name?"
One field is "what would you like to be called?"
You don't need to try to infer one from the other.