What is the term for an association of individuals united for a common purpose and permitted by law to use a common name?

The term that describes an association of individuals united for a common purpose, which is also legally permitted to use a common name, is a corporation. A corporation is a legal entity that is distinct from its owners, allowing it to engage in business, enter contracts, and incur liabilities in its own name.

Corporations are formed under the laws of the state in which they are incorporated, providing them with certain legal protections and benefits, such as limited liability for their shareholders. This means that the personal assets of individual shareholders are generally protected from the corporation's debts and liabilities.

In contrast, while partnerships and cooperatives are also forms of business associations, they do not provide the same level of legal distinction and liability protection as corporations do. A cooperative is specifically a member-owned enterprise, whereas a franchise involves legal agreements granting rights to operate a business under a brand, but does not denote a distinct legal entity for the group as a whole. Thus, the notion of a common name and the legal privileges associated with a separate legal entity are hallmarks of a corporation.