religion question?

I am catholic and Dh is jewish.. we are baptizing the twins catholic but DH's grandma wants to have them put in the book of life and named with Hebrew names. Do you know if this is an issue with the church at all? My church is pretty strict where both godparents have to be catholic and show their documentation. When you are given a Hebrew name is that the equivalent of being baptized into the jewish religion? Sorry I'm so clueless, just confused

Thanks so much!