A name like that screams new money / no roots to me.

There is a big difference between uncommon names but with deep roots like the above mentioned Sixtus and completely unique names X Æ A-12.

The former is very common in the upper classes, the latter not so much.

Being rich doesn't make you upper class, evidently.

If your first name is really henrik, that would be pretty unique in the English speaking world. I think what you say might be true for your country but not really in others. Many upperclass people have unique names in the United States (and also in Britain I think ). In fact it used to be quite fashionable with some upperclass people to have a vaguely foreign sounding name especially one hinting at some kind of European connection.

Maybe not in Europe (and that is arguable depending on the country). In the US it absolutely does.

No.

Here's a good resource if you want to read up on how class works in the US: https://siderea.livejournal.com/1260265.html