I can't say without more information, but I can mention a few of the legal principles involved in disputes like this.
First, claiming damages generally requires that the plaintiff have actually sustained provable, quantifiable money damages. There are a few instances where a plaintiff can recover damages because injury is presumed - such as trespass to land - but the damages awarded, absent proof of actual injury, are nominal ($1 or so). Also, there are a few situations where a statute authorizes an award of money damages absent proof of harm to the plaintiff in a particular sum.
Next, various laws restrict the right of a business to call itself by someone else's business name. These include Federal trademark law and California's unfair competition statutes, and perhaps others (such as tort law principles covering intentional interference with prospective business advantage). These laws also have prerequisites that must be met before a successful suit or claim can be made. With Federal trademarks, there is a requirement to register, and that in turn has requirements, such as showing use of the trademark in interstate commerce, which is a major hurdle for a landscape business. Unfair competition would be hard to show with businesses as different as landscaping and advertising.
Also, examples are numerous of same-name companies in different businesses, co-existing peaceably in the same trading area. Just opening my phone book to the business listings at random, my eye first caught "Sterling Construction" along with "Sterling Graphics" and "Sterling Rainbow Pool Center."
It's possible that your agreement for the former business relationship included an express or implied promise that the ad company would stop using your name when the relationship ended. This would perhaps entitle you to get an injunction against them, based on breach of a contract provision. However, getting money damages under any theory is probably going to require that you document (plead and prove) how much you were harmed, in dollars.
