No. If the client name is listed they would be slammed with emails from all over begging to be hired for the project. Similar incidents have happened in the past when the client inadvertently put their contact info in the job posting.
If the client has made at least five hires, it's in someone's feedback or the job description. "Need a logo for Greg P Associates in Boston" is pretty specific. Also, "Greg P at GP Associates is a great client!" With a few clues, I can find the name even without that. "New firm in Boston specializing in fly excrement purification needs ..." How many can there be?