Generally speaking, this would strike you as more indisputable if you come from a rich family like David Frum does. This is not to say that there is anything wrong from coming from a rich family: a large fraction of the high achievers in history had a little (or a lot of) family money improving their options.
Pseudonyms seem to be in decline among major celebrities from the 18th Century when most writers chose pseudonyms. For example, we still don’t know the identities of the Anti-Federalist pamphleteers of the late 1780s, even though (or perhaps because) their suspicions about the long run consequences of the Constitution have largely been proven accurate.
The only sisters to win Best Actress Oscars, Joan Fontaine (who died in 2013 at 96) and Olivia de Havilland (who celebrated her 101st birthday a few weeks ago by filing another lawsuit, this one over her portrayal in a TV series about Bette Davis and Joan Crawford), sound like the latter must have been a pseudonym. But in truth, the two actresses were paternal first cousins of famed aircraft designer Captain Sir Geoffrey de Havilland, while Fontaine was instead their mother’s maiden name.
The reasons that, say, George Orwell or Joe Strummer chose pseudonyms (to avoid embarrassing their respectable families and to avoid raising questions about their own respectable class backgrounds) are perfectly reasonable. Ever since John Milton, we’ve been aware that more speech is better than less speech, so pseudonyms are good for facilitating more speech. There doesn’t seem to be any reason to assume that anything said under a public name is more or less reliable than anything said under a pen name.
When I started writing professionally a little over a quarter of a century ago, I seriously considered using a pseudonym like Eric Blair / George Orwell. But I couldn’t figure out how to cash checks made out to a pseudonym, so I eventually junked the idea. But I generally wish I had gone with a pen name, for reasons that are obvious at this point to me, but I won’t mention them because they are so obvious.