Is it possible to copyright a work in the name of a fictional writer? For example, like Nicolas Bourbaki or some pen name of some author? Can I use my own fictional name to copyright the work?
Yes, at least you can in the United States.
Reference: U.S. Copyright Office - Pseudonyms
Also: there are two ways you can indicate your pseudonym with the Copyright Office. You can either use just your pseudonym or you can use your real name and indicate you are "writing as pen name." Using the pseudonym as the copyright claimant can pose potential legal problems should such issues arise, so the Copyright Office rightly suggest that if you go that route, you should check with legal counsel.
Keep in mind, too, that because of tax requirements for payment, if you receive payment from a publisher, they will have to have your real name and social security number, unless you can work out some "middle-man" arrangement with an agent.
Finally, using a pseudonym doesn't offer any legal protection if you were, for instance, sued for slander or plagiarism.