I'd list the alternate business name on your resume, but I wouldn't outright lie about what it was (saying that it was a restaurant or something like that). (careerdigital.com)
While a little exaggeration will do no harm, telling outright lies on your profile is a big no - no. (dating-sites.bestreviews.net)
Promoting your business is one thing; telling outright lies in order to garner press attention or to save face is another. (entrepreneur.com)