Hispanic Name Traditions?

My fiance is half mexican. His grandmother's name is Maria, and his family wanted us to make our first born daughter named after her.. so i made her middle name Marie . Leigh, is my familly name that I wanted to name her after, but due to their religeous beliefs , i just figured i would name the next girl ( if we have one ) , after my side .. & i can 't really combine Leigh & Marie bc they rhyme ? - well , i was just recently told that ALL of our children will have Marie in the name . which isn't fair to me at all .. i hold the baby , i have the baby .. they will have his last name of course , & my first born has their tradition instead of mine . am i in the wrong for not having marie in the next name ? ... i am American / Australian .