Naming a business can be just as challenging as naming a youngster, but there's more to a name than what you print on the business card. For starters, you could put your own name on the business. After all, what are the chances that there's another plumber named Smith who is thinking about setting up shop in your town?
If your own name won't work (Leaky Plumbing may not be the best choice), you may have to be more creative. Yourtown Heating & Air is probably taken. So is AAA Air Conditioning, so you might consider something more general such as Citywide or A Plus Plumbing Service. Chances are these names are taken, too.