My wife’s father is not jewish, but her mother is 100% jewish. in our ketubah is written her name and her mother’s name, like Chane Gitl bat Faige Malke. Is it correct? Because the halacha says, that it should write her father’s name! like hane gitl bat george.

It’s okay. There are other opinions as well that don’t write any parents name, but your ketubah is good. The father's name in any case should not be entered.