(a) The participating health insurers may issue the group insurance policy in their own names or in the name of an unincorporated association, trust, or other organization formed for the sole purposes of this chapter and evidenced by a written contract executed by the insurers. An unincorporated association, trust, or other organization formed under this subsection may sue and be sued in the name of the association, trust, or organization.
(b) A person licensed as a general life, accident, and health agent under Chapter 4054, as a general property and casualty agent under Chapter 4051 authorized to write health and accident insurance under Section 4051.053, or as a personal lines property and casualty agent authorized to write health and accident insurance under Section 4051.402, may act in the licensed capacity in connection with an insurance policy or a certificate of insurance issued by an unincorporated association, trust, or other organization formed under Subsection (a). The agent is not required to notify the department that the person has been appointed to act for that purpose.