...giving him a multi-barelled surname to boot! Though I'm not sure if that's a stereotype in the US?

I'm not sure what stereotype you're referring to, but the length of Harry's surname reads to me as almost a parody of the inclination to signal egalitarianism. I take it as evidence that his adopted parents (particularly the father) are Very Liberal, but that's all.

Class, Americanization

I hadn't actually noticed that particular issue before, but now that it's been pointed out, it seems to me more like a LessWrong-related bias than an American one. We like to focus on big, progressive, constructive issues, and upper-class people are in a better position to do so meaningfully; stories with disenfranchised characters are more likely to deal with apartment cows like 'how can I keep my abusive stepfather from attacking me' and 'how can I afford to replace my broken wand', which we don't generally like to think about.