Power Of Agreement
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.
Conventions and Treaties signed by signatories of states bind private actors to the terms of that agreement through the domestic application of the treaty provisions. These agreements may be bilateral (between two countries/states) or multilateral (between three or more countries/states).