Names and cultural differences

My boyfriend's family asked if I have started thinking about names, and I said I only know for sure that for a girl it will be japanese first name, American middle name. For a boy, American first name, japanese middle name. 
They don't think I should have japanese names because the baby will be made fun of growing up. And they think it's weird I want to send the baby (when he/she gets older) to Japanese saturday school. 
It's very important to me that my child(ren) are immersed in their culture, especially because I live somewhere so whitewashed. I don't want them wondering where they come from. 
I guess this is more of a rant than anything, but anyone have opinions or thoughts?