Yes, you can write under your real name. Such use is not trademark use all on its own. It matters not whether there are other authors by the same name.

Can there be two authors?

A Work by Two Authors: Name both authors in the signal phrase or in parentheses each time you cite the work. Use the word "and" between the authors' names within the text and use the ampersand in parentheses.

Can two book have the same name?

The answer, as the books below show, is yes. At least in the United States, book titles are not copyrighted and, aside from internet searches, there's no surefire way to figure out if your book will have the same title as someone else's.