A pen name is a name an author publishes a book under. It isn't their real name, it's only the name they go by when writing books.
Many female authors used male names to publish their books in time periods such as 1700s or 1800s, when women weren't thought of as smart and they didn't have rights. The male names were their pen names, used so that people would respect them.
<em>Examples in modern day (pen name --> real name):</em>
J.K. Rowling (Harry Potter) --> Joanne Kathleen Rowling
Lemony Snicket (Series of Unfortunate Events) --> Daniel Handler
Pretty sure it's the First and Third sentence.
You need to give more context. I will help when you do. God bless!