You don't say what make you think he has run with your deposit - many contractors take a deposit and don't start work for a month or more, especially if custom cabients or countertop or such have to be ordered and delivered, and most like to book work 2 or more months in advance so maintain a steady workflow.
Have you talked to him on the phone about start of work, or made a "legal" attempt to contact him - by certified mail, return receipt, demanding your money back for lack of performance ? If not, then the police and so forth should tell you that you have not done your part - without failure to perform by a contract specified start date, or failing to finish by a specified completion date, you probably have no case yet, and could even be sued for false arrest if they did arrest him. Certainly, without a failure to do anything on the job on a specified start date, there would be no fraud.
Having multiple names on the same license is not illegal in some states, and is actually common in states where for instance a master plumber is required for a plumbing business, and one old master plumber acts as master plumber for multiple companies, supervising (hopefully) a number of journeyman and apprentice plumbers in several different companies. I had a job once where, because it was a large job, we identified 5 different in-state blasting companies as potential bidders for a large precision blasting job - at the pre-bid conference one man showed up - turned out he was the licensed blaster for pretty much every blasting and excavation company in the state, and just moved from job to job to do the explosives and blasting work while the different companies did the excavation, concrete, and such.
The working out of homes is certainly an indication you are talking a small company, but not an automatic red flag - there are many viable and responsible companies, generally sole proprietorships, who operate out of the owner's home. I can think of several offhand locally that do so and I would think certainly turn well over a million $ a year in gross receipts.
If you are sure there is funny business going on here, I would do some research and get your eggs in a row before filing formal complaints, though you could certainly ask several agencies if they have been getting complaints about this individual/company.
Several of the other comments refer to the Consumer Protection Agency - they might be able to help, as might the police or your local District Attorney's Office, or state Attorney General's Office Consumer Fraud division.
For action against him if this was a profession that requires licensing in your state, though it will commonly not get you any $ back, the state licensing board or equivalent is what you want. Getting a conviction from them against him for unethical or unlicensed operation would support a civil fraud case, because you would then have him (if he was unlicensed but should have been) for fraudulent misrepresentation, in many states. Google a phrase similar to this to find the board website - Nebraska Plumbers license board
I presume he was not licensed or bonded - for this type of case, both might be responsible to cover him for a fraud related to a contract, assuming you even have a legal contract at this point, which might also be in doubt since you said all you had was a receipt. This puts you in a real bad situation, because without a contract for performance including price and schedule and scope of work, it is your word versus his about when he was supposed to start, what the work scope was, etc.
If he is still in town and you can contact him and imply he has faild to perform and you want your money back or you will notify authorities, he might give the money back to avoid legal trouble. If you can prove he has skipped town, then your fraud case gets stronger, but of course pursuing it gets a lot tougher.