You, an employee, or an agency — Google Business Profile lets an owner add multiple managers and owners to the same profile, so it's never an all-or-nothing decision. Add yourself as the primary owner, then invite a manager (an employee or an outside marketing partner) to handle day-to-day posting, review responses, and photo updates without giving up ownership control.
Most contractors start by managing it themselves and add a manager once posting consistently becomes a burden rather than a habit. The profile itself stays free either way — what you're paying for, if you bring in outside help, is the discipline of someone actually keeping it active every week instead of it going stale.
Go deeper
Full breakdown: Google Business Profile Management