Well if you are really bothered about it, OP, I don't suppose it is unreasonable. You can't help your feelings.
I wouldn't matter at all to me though. My DS has his father's surname and not mine (we are married but I kept my own surname). So we are in the same position, OP - and my child has a first name from one part of my culture and a surname from his father's.
Ultimately, my DS is our child and I don't feel he is less of one culture or another based on his name.
As it happens, I look incredibly like an English Rose rather than my full varied ethnic and cultural makeup - does that make me less part of other cultures because a quirk of genes makes me look a certain way?
Ultimately your DD will be a mix of backgrounds like most people. That's a great thing and I never had any problems understanding that I was the product of a variety of cultures.
Equally, it doesn't really matter that because I look a certain way, I generally have to tell people about my background or they think I am probably of English origin.
So of course you can change her name if it is really important than anyone who meets her knows immediately that she is part British in origin. Or if you wish you shared a surname with her.
But otherwise I wouldn't personally feel it was that important.