Shakespeare very likely asked this question as well–though I’m sure he did it with more eloquence.
Whether or not to use a pseudonym (a pen name) is a question pretty much every writer asks themselves when considering publication. There are plenty of reasons to use one, and just as many not to. Tess Grantham, an Alchemy member and one of my closest writing buddies, discusses the reasoning behind her decision to use a nom de plume here on her blog. Good reading for anyone considering it!