This whole issue raises a lot of predicaments. I speak 4 languages, I have a keen interest in linguistics and the origin of names, and I've lived in 4 countries on 3 different continents. When I come across someone with a non-English name, if the circumstances are appropriate, I will ask them about it. It's because I am genuinely interested. I'm not trying to get them on the next deportation flight. I have always enjoyed learning from them, as I can now more easily recognise and pronounce names from certain countries, and they have always seemed to welcome my interest.
I'm probably quite tactful in my approach to it, as opposed to Lady Hussey, but where does this end? With nobody being able to ask anyone about their heritage, unless you've asked them in the universally approved manner and registered yourself as a definite non-racist with the government database?