Joining a white fraternity when half white half asian?

I want to join a fraternity at my college. I go a pretty mid sized college that only has white fraternities. I know race isn't a factor but when I look at the pictures of past members, I never see an asian/black guy or a name that isn't white. With that being said, I have an indian name because my dad is indian and my mom is white. I want to join a fraternity but I dont know how welcoming they will be to me if I am not completely white or have a white name.