[I've edited to make this tighter.]
A solo cannot describe his or her practice with the phrase "and Associates" if in fact there are no associates there. It's false and misleading. There's not much more to say on whether or not the firm name was deceptive.
The story also raises the hypothetical issue of whether Sotomayor could have called her practice "The Law Offices of Sonia Sotomayor." (Notice the "s" at the end of "Office.") I raised that issue on two legal ethics listservs, both of which are full of ethics gurus, and there was wide disagreement. (When I opened my solo practice, I chose the safe route of going with "John Steele, Attorney at Law.")