According to Chicago Style Manual (16th ed.), "In whatever form interviews or personal communications exist -- published, broadcast, preserved in audiovisual form, available online -- the citation normally begins with the name of the person interviewed or the person from whom the communication was received. The interviewer or recipient, if mentioned, comes second."
"The absence of a name should be explained. (e.g., 'All interviews were conducted in confidentiality, and the names of interviewees are withheld by mutual agreement.')."
In text:
In a telephone conversation with the author on January 6, 2015, President John F. Kennedy admitted that...
In a note:
2. Constance Conlon, e-mail to author, April 17, 2014.
Unpublished Interview:
8. Andrew Spock (Dean of English department, Dixie State University), in discussion with the author, September 2014.
Published/Broadcast Interview:
Bellour, Raymond. "Alternation, Segmentation, Hypnosis: Interview with Raymond Bellour." By Janet Bergstrom. Camera Obscura, nos. 3-4 (Summer 1979): 89-94.
Letter/Memo (archived):
12. Memorandum by Alvin Johnson, 1937, file 36, Horace Kallen Papers, YIVO Institute for Jewish Research, New York.
Letter/Memo (not archived):
18. John Smith to Susie Smith, 2015, in the author's possession, St. George, UT.