You may want to have an attorney review and make suggestions on a template of your business contract. An attorney can pinpoint issues for your particular business that you may need to include in the agreement. You can use a business agreement template and modify it to fit your needs, rather than writing the agreement from scratch.
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.