Business-name infringement cases can be prosecuted in California on not mush more than inherently unfair competition. The results are fact-sensitive, having a lot to do with whether the new user's taking over of the old name (a) usurps goodwill, or (b) may result in marketplace confusion. If you are sued, it would probably be is state court; there don't seem to be any federal issues here. I'd say the chances of a suit are well under 50-50, and if there were one, you'd probably win. However, as I say, unfair competition is very fact-dependent, and the facts you should re-check are (a) anything alleged in the cease-and-desist letter; (b) relinquishment of the LLC name - by dissolution, suspension, or what?; and (c) whether any significant number of potential customers associate the current business with the former names. For example, I can still remember the names of the owners of the real-estate firm that sold my parents a house 40 years ago, and the firm name is still in use by someone. My inclination would be to resist or fight back if I were in your position, but not without going over the factual background again, carefully.

The first thing he should do when receiving a letter like this is go to a competent intellectual property attorney and show the attorney the letter. While it is possible to discuss general principles in a forum like this, the cases are fact-specific and without knowing the exact players and names involved, it's hard to give specific advice.

In general, if the name being used was never registered as a trademark or business name, and the purchasing company never used them, then it would have a hard time showing infringement. If the person using the mark was the seller of the business, then the case becomes stronger because that person has relinquished rights by contract in exchange for payment.

What also matters is whether the business name being used is the former employee's name (and he wasn't the seller of the business), or is he just using the name because of its market value. It would be hard to prevent a person from using his own name in the name of the business if that name had never been registered. However, if the name being used is a "made up" name to exploit another company's pre-existing marketing and reputation, there's a good chance it would be considered infringing even without a prior registration.

As far as the domain name, if the company previously owned it, never used it, and let it lapse, then they should have to pay to get it back. If it goes to court, the court might require the company to pay any costs the new user incurred (such as registration and transfer fees) but could require the transfer. Again, everything here is fact-specific.

If this is an actual situation you're involved in, you should go to a lawyer sooner rather than later, because there may be time limits to respond.