You probably don't have to deadhead them. It isn't likely you'll get reseeded volunteers in your zone. Chances are the seeds won't ripen to viable, and the birds love them, ripe or not.

Do you know which cultivar you have?

Thanks for the help Donn. No I don't know what type this grass is other than a fountain grass. :) It is so beautiful. I am starting to really like grasses. Never used them before.