Suddenly I’m put in mind of a great exchange from All in the Family:
Archie: That’s something the Hebes do. They change their last names but keep their first names so that they’ll still recognize each other.
Mike: What the hell are you talking about?
Archie: Well, you get two Jews meeting on the street. One of them says his name is Smith … Izzy Smith. That’s how it works, see? So you get Sol Nelson, Morris Jones…
Mike (dryly): Abe Lincoln.
Edith (astonished): I didn’t know Lincoln was Jewish!
AARGH! No wonder I’m not rich! I chose the wrong last name! 
Zev Steinhardt
<quibble>
Smith, White, Miller, and most of the other English names mentioned are Germanic. English is a Germanic language. It has borrowed many non-Germanic words, but those are not among them.
</quibble>
My anecdotal experience is different from your anecdotal experience. Just off the top of my head I can think of Jewish families of my acquaintance named Brandon, Metcalf, Miller, Shore, and Jackson.
Yes, I’d say that the Jews I know who have non-anglicized Teutonic or Slavic or Semitic names (including the ones in my own family who share my own extremely non-anglicized name) probably outnumber the ones with anglicized names. But I certainly wouldn’t call the latter category “rare”.
Am I the only one who’s never heard of Diamond or Dimastein as a last name?
Also, I don’t get Archie’s scheme at all. How are they changing first names?
Never heard of Neil Diamond (awful popular musician) or Jared Diamond (awful popular author)?
Irene Diamond was a major AIDS benefactor through her Aaron Diamond Foundation (named after her husband). Also found the spec script for Casablanca back in the 1940s, I believe. And you may remember actress Selma Diamond from Night Court, the gravelly-voiced bailiff. Well, the first one.
They’re not, that’s the point – the hypothetical Sol Nelson et al. are keeping their first names but changing their last names.
Man, I’m really missing that happy Jewish guy smilie right around now.