Who is the official with the authority to formally assume responsibility for operating an IS at an acceptable level of risk to agency operations (including mission, functions, image, or reputation)…

The Authorizing Official (AO) is precisely the individual defined by NIST and other frameworks as having the authority to accept the risk associated with an information system and grant an Authorization to Operate (ATO). The question explicitly states 'formally assume responsibility for operating an IS at an acceptable level of risk' and mentions 'Synonymous with Accreditation Authority,' which are key characteristics of an AO.

An Information Security Architect designs security solutions but does not typically hold the formal authority to accept overall operational risk for a system.

An Information System Owner is responsible for the system throughout its lifecycle but does not typically have the ultimate authority to formally accept the operational risk for the agency.

A Chief Information Officer (CIO) is a senior executive responsible for an organization's IT strategy and operations, but while they may oversee the RMF process, the specific role of formally accepting risk for an individual system is usually delegated to an AO.