Why do some authors use Pen name instead of real name?

To hide their identity. I have a couple of friends who write and use pen names.

Reasons vary:

They work in the public eye and don’t want their real life audience to know about what they write.

They don’t want their current employer to know what they write.

They don’t want their friends to know they write.

They want to write as a male when they are female, or vice versa, because they feel it will be better revived.

I always thought if I wrote a book I would use a pen name.

For many it’s the same reason why many actors use a stage name. Certain names just stand out more and are more “bankable”. “George Orwell” stands out better on a book cover than “Eric Blair” does, “Natalie Portman” has more star power to it than “Neta Herschlag”.

Lots of reasons.

I never managed to come up with a pen-name when I was young and had aspirations of being a writer, but I knew I didn’t want my rhyming name on a book cover. It just didn’t have the right “flow”, and I can’t stand the spelling of my given name. My married name now, great for a construction company (strong and honest-sounding), not great for a writer of whimsical fantasy stories.

Sometimes for privacy, obviously, and sometimes if a known author writes something in a different genre he will change his name so that people don’t pre-judge the book based on his other works. If Stephen King wrote a self-help book, for instance, he might be better off using a different name…often, he will “leak” the connection later, which will cause book sales to boom, as well.
As others have mentioned, sometimes it is simply because he doesn’t feel like his name is recognizable or saleable- or perhaps he has the same name as a well known author and wants to avoid confusion.
Changing to a pen name because you had a foreign or weird-sounding name was common in years past, today it is getting much more common to just keep your name and “celebrate your weirdness”, which I consider a good thing.