I'm having a small ceremony in San Francisco and I'd like for it to be at Shakespear's Garden. I don't need the whole garden. If I don't care who else is in the park besides the small group attending my ceremony is it necessary to rent it?

Yes, it would risky not to just in case someone else actually reserves the space for the same date (particularly if it’s a weekend).

I'm not sure if it is necessary to rent it if you don't care who is in the space. I'm not even sure if they prevent the public from entering during weddings (other than the space you have set up for your ceremony). Check their website/ call and ask your questions if you can't find the information you desire. http://sfrecpark.org/reservablefacility/golden-gate-park-shakespeare-garden-wedding-site/