Can a person register an LLC / company in the United States with the name of a fake company from a video game or comic book series that was created in Japan?
Yes, if it's not already in use by someone else. Check the Secretary of State website http://kepler.sos.ca.gov/ and search for the name. If it's available, you can register it, or reserve the name for a short while until you're ready to register.
Disclaimer: Please note that this answer does not constitute legal advice, and should not be relied on, since each state has different laws, each situation is fact specific, and it is impossible to evaluate a legal problem without a comprehensive consultation and review of all the facts and documents at issue. This answer does not create an attorney-client relationship.
A limited liability company or corporation name may be adopted if the name is not the same as or too similar to an existing name on the records of the California Secretary of State or if the name is not misleading to the public.
You can check name availability by sending in the following form to the California Secretary of State: http://www.sos.ca.gov/business/corp/pdf/naavinquiryform.pdf
However, just because you are able to register the LLC name in California does not mean that you won't be liable for trademark, copyright or other intellectual property right violations.