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.
If you write under a pseudonym and do not want to have your identity revealed in the Copyright Office’s records, give your pseudonym and identify it as such on your application. You can leave blank the space for the name of the author.
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.
Of course that depends on the country and internal laws but, since there may be Brazilian and Portuguese writers here, I'll answer based on those countries.
I just registered a book with IGAC, the institute that handles such requests in Portugal and it required my real name — which makes sense since it has to track who I really am — and my pen name — Eduardo Fernandes — which I think is for public consult of the archives.
If you want to use only the pen name, it's not possible, which — in my opinion — makes all the sense since no copyright institute can register a manuscript without proper documentation and, if they have your documentation, even if they would accept your pen name only, they would also have access to your real name. I don't see how it's possible to copyright a manuscript without knowing who — in legal terms — you are.
Of course, you can create your own legal fictional identity — for example, a small one-man company — and let the company have the rights on your work, not you. That would make the YourPenName Company be displayed as the owner, not you. Of course, again, your company will need to have papers and you would be listed as responsible for it, which would make your real identity findable.