Who Can Sign - For partnerships, only general partners can sign a contract, not a limited partner. For LLC's, a managing member or a hired manager can sign. For corporations, the company's president or chief executive officer is presumed to have the authority to sign. For an organization or association, a board president would have the authority, but may require a vote of the governing board to approve the deal.
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.