No, your job title does not have to be office manager to meet the requirements. However, you must meet the veterinary practice management experience requirements outlined in the application.
The application details fifteen (15) duties common to most veterinary practices. Candidates must have performed at least thirteen (13) of the fifteen (15) listed functions for at least one (1) year within the preceding three (3) years to qualify as having the necessary management experience needed for certification. The fifteen duties are outlined on the CVOM program page here.