9-8-8 Implementation Act of 2023 This bill modifies programs and activities that support access to behavioral health services, with a focus on crisis services and the 9-8-8 telecommunication system that provides callers with mental health or suicide crisis support and resources. For example, the bill establishes a national suicide prevention media campaign and grant programs to support crisis call centers and the behavioral health workforce. It also requires the Department of Health and Human Services to convene a panel to develop recommendations for 9-1-1 dispatchers on how respond to callers experiencing behavioral health crises, including with respect to utilizing the 9-8-8 system. The bill also expands coverage under Medicare, Medicaid, the Children's Health Insurance Program (CHIP), private insurance, and insurance programs for members of the Armed Forces, veterans, and federal employees to include crisis response services.