I don't mind my first name, maybe not be my choice, I know full well that there are worse out there.
Our sons were given an 'English' first name and then a middle name from hubs country. Years ago we weren't sure where we would definitely settle , so at least they had a name that could've been use if we had gone to live in hubs homeland
I don't think your children will have difficulty integrating. My friend who's black was very annoyed when she first lived here. This is an area where Monday club (some conservative area!) was very active. In fact, last election saw far -right National Front and BNP voted in. My son kept saying to me that I need to colour or bleach my skin and the Caucasians can be very nasty to me! True. I just wouldn't let them spoil my day! Of course, not all whites are like that. One lady was very nice and always asks after my son, knowing my son had some difficulty in the primary school the end of her road.