Well, I think what would happen is that your "pen name persona" would have a higher threshold for being able to claim defamation, and that could spill over to your real name.

For instance, you publish as Bill Smith, but your real name is John Jones....well "Bill Smith" can then be publicly talked about, criticized, speculated about, etc....One of those speculations might be: "Its a fake name, his real name is John Jones".

To add to this, even if you are famous (ie. a public persona) you can still sue someone for defamation. The difference is in the threshold for "actual malice".

Basically its assumed public people are going to be speculated about, so of a politician you can say: "Biden probably was involved with stealing money from Ukraine". Joe Biden as the President would have a very very high threshold to prove "actual malice"....whereas if you say that about a private persona the threshold would be far lower.