An investigation that consists of checking the records of appropriate federal agencies for information bearing on the loyalty and suitability of a person under investigation is known as a(n):

The process described involves conducting a thorough check of records from relevant federal agencies to assess an individual's loyalty and suitability for a particular position or role. This is specifically referred to as a National Agency Check. This type of investigation is crucial for positions requiring a security clearance, as it seeks to uncover any supporting or disqualifying information that could affect an individual's eligibility.

A National Agency Check typically includes background checks against multiple federal databases, including those maintained by the FBI, which provides criminal history and other relevant data. However, the term itself is broader than just being an FBI investigation. While it encompasses many aspects related to an individual's loyalty, it is distinguished from loyalty investigations, which are more focused solely on an individual's allegiance and commitment to the country or organization. A background investigation, while similar, may not solely rely on federal agency records but could include other sources of information as well.

Thus, the National Agency Check is the most precise term that describes the investigative process of reviewing federal agency records to evaluate the loyalty and suitability of an individual under scrutiny.