>利益なくても架空のビジネス名でも大丈夫のようですよ。
大丈夫じゃないと思いますよ。
Excluded businesses
An enterprise, corporation or organization is not a Canadian business if it exists primarily to allow permanent residents to comply with their residency obligations during a stay outside Canada.
http://www.cic.gc.ca/english/newcomer/cdnbusiness.html