Odds are good that you’ve at least considered writing under a pen name at some point or another. One issue that might be holding you back is the question of copyright. Not to worry, though — even if you use a pen name, you enjoy the protections of copyright.
Just like any other work, pseudonymous writings are considered copyrighted whether or not you register them. There are a few differences in length of copyright, at least in the U.S, if you use a pen name: rather than remaining under copyright until 70 years after the author’s death, a pseudonymous work is protected until 95 years from the initial publication of the work, or 120 years from its creation, whichever term expires first. You can still get that longer copyright for work written under a pen name by registering it with the Copyright Office — which has a handy Pseudonym Factsheet.
It’s up to you to decide whether registering your work with the Copyright Office is necessary: it depends more on whether you expect to need to defend it than anything else.