Hi Mary,
Thank you for your sunflower pest question. Without seeing the insect, I cannot definitively determine what is causing the damage to your plants from your photos, however, it may be leaf beetle. The following articles provide information on pests in sunflowers and management options. Photos of leaf beetle damage are included so that you can compare to your plants:
Managing Pests in Gardens: Floriculture: Sunflower—UC IPM (ucanr.edu)
Landscape pests-Leaf beetle | Pacific Northwest Pest Management Handbooks (pnwhandbooks.org)

If you need additional information, I recommend you contact the Plant Clinic at the OSU Deschutes County Extension in Redmond. You can call the phone number listed below or send your photos and question to <personal data hidden>

The person on duty will review your information, conduct necessary research, and contact you with findings and management options.

Summer Hours: Monday through Thursday, 9:00 to 5:00 pm, Friday 9:00 am to 1:00 pm.

Phone:<personal data hidden> x79630

We always welcome your home garden questions at the OSU Plant Clinic.