Your pen name is your brand. Just like any brand, it should be protected. I only write articles showing my own name for my website. When I supply ghost written articles, I do not brand them with my name.
Personally, I feel that by name should only be used to promote my own services and my own website. I do not lend out my name or for that matter my content to others. I want to retain close control of my brand and my intellectual property. Before you write for someone else under your own name you may want to consider these important points.
1. Will the content you supply be changed in any way after you provide it? If it will be you may not like the changes or the meaning of your original piece may be different.
2. Is the site where your content will reside a good match for your ideologies? How about types of advertisers? Remember your name will give credibility to the site. Are the products and services one with which you would want to be linked?
3. If you are writing under your own name, remember the Internet archives all content literally forever. Will joining your name to a site or cause be a problem in the future for potential clients or job opportunities.
4. You may even want to consider receiving a higher level of compensation for any pieces that you write for other websites using your own name.
Once you let something go, it is nearly impossible to get it back again, that goes not only with your reputation, but with the value of your own brand or pen name.