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.
Naming the Parties - You begin the contract by naming the parties in the agreement. This may seem obvious, but attorney Mark Cohen of Colorado writes in his article Ten Things to Consider Before Signing a Contract that "a common error is to use the name of a person representing an entity rather than the name of the entity."