You can trademark the name alone, without linking it to any specific logo. Click on
United States Patent and Trademark Office Home Page, go to trademarks an read. Learn to use the search facilities. Use help under the search facilities.
You can not trademark too general terms. "Famous" is used already in different contexts, so you cannot register "Famous" alone.
Try to enter the search string: live[ld] and famous[bi] and "025"[ic].
You'll get 52 matches for live registrations for apparel, where "Famous" apperar in the basic indices.
Even abandoned/dead registrations can sometimes block a new registration.
Also, don't rely on copyright on names, titles and simple phrases, as these cannot be copyrighted. If you want to protect these kind of slogans, they must be trademarked.