Ensuring Fair Access to Veterans Healthcare Act This bill establishes in the Veterans Health Administration an Office of the Ombudsman, which shall: investigate and resolve complaints made by or on behalf of patients receiving medical care or hospital services at a Department of Veterans Affairs (VA) medical facility (covered patients) that relate to action, inaction, or decisions made by VA employees that may adversely affect such patients; assist covered patients in finding patient advocates, veterans service organizations, or other similar entities to advocate for their health, safety, welfare, and rights; ensure that covered patients have regular and timely access to Office services; administer the reporting system provided for by this Act; and provide training to local ombudsmen and volunteers. The Office shall establish a reporting system to collect and analyze complaint data in order to determine how to resolve significant VA medical facility problems. Each VA medical facility shall have a local ombudsman responsible for carrying out the duties of the Office at such location.