Also for international users browsing in English labeling the fields "given name" and "family name" are way more clearer than using first and last names.
Exactly what I was thinking - plus a field to state the order they should be displayed in seeing as Asian cultures usually state the Family Name first.
What do you mean "the legal surname"? I'm Spanish and my legal name is my full name with both family names. You can't just ignore one. Also, Spanish people have two family names, but they can be composite, so they may look as three or four family names.
However, most people are usually known by one family name, but which one is used depends on which one is more easily recognizable.