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Jan, you pose an interesting question, particularly with regards to names. (I hope it's about names, because if she had asked, say, Marcus Rashford where he was from, I would think it was triggered by his colour.) I don't know for certain where the line is to be drawn in terms of etiquette; I would be comfortable saying to Ms Raducanu "that's an unusual name, where is it from?" (in fact we've just done as much whilst watching the footie and saying "oh, Mac Allister isn't your average Argentinian name"), whereas I wouldn't ask Mr Patel where his name was from. I think the difference is that Raducanu is uncommon here and Patel isn't.
I have a name that's uncommon in England (yes, yes, not Button, the other one) but very common in Scotland. I don't actually mind being quizzed on it but of course you don't know that until I tell you, so I guess you ask once, see how I respond and drop it if I indicate I don't like the subject. At least she didn't ask me "are you related to the Hertfordshire Buttons" sort of thing (which would be a bit snobby but not what one would call racist - unless one comes from Hertfordshire obviously).
Seems to me as though Lady Hussey could at least do with a revision course on good manners, even if she had the wit to avoid asking her host "where do you Battenbergs come from then?"