Uh I'll write slow so you can keep up
1) If you are flying internationally from the US your ticket name must be the same as the name on the passport.
2) The name on the passport does not have to match the greencard.
3) OP wife will not be allowed to board if her ticket name does not match passport name.
4) She may be denied boarding even if the ticket name matches the passport name if:
5) The destination(this time Mexico) requires a visa for a passport holder from the Philippines.
6) Full stop.