I need to fill in some applications for Green Card(USA). My daughter has two names in Greek, I can't figure out whether that's two first names or a first name and a middle name for the American documentation.

I do not mean to be "rude" but if you don't know what and how your daughters name is, we don't. If she has two first names, then she has two first names, being in Greece or the US does not change how her names are listed on a birth certificate.

The baby is Greek and very many people in Greece have 2 names but they don't have what the Americans call middle name, they just give a general definition of name, and as far as I can see, the Americans usually don't have 2 first names. The Greek birth certificate only says name and both her names are written under it with a hyphen.