If you run a business as a sole proprietorship, it would be appropriate to be identified in the contract as John Jones doing business as Jones Plumbing. If you organized your business as a Limited Liability Company, identifying your participation in the contract by your name could remove any personal liability protection that an LLC provides. Similar issues can arise with a partnership if each individual is identified as a party to the contract.
Legal Contracts - Under state laws, only a few category of contracts must be in writing, such as a mortgage contract or contracts covering more than a year. It's still a good idea, however, to have a written agreement for business transactions beyond an ordinary sale of goods. There is no law requiring a lawyer to write your contract. If the transaction is relatively simple, the contract can also be simple. But you also have to pay attention to certain details to avoid issues arising later.