What happens if the Marietta home I want is listed by my own agent's brokerage?

Georgia allows designated agency in this situation, where your agent and the listing agent are separate people at the same brokerage, each representing only their own client. The brokerage itself stays neutral while the two designated agents negotiate on your behalf and the seller's, and this setup should be disclosed to you in writing before you make an offer on the Marietta home. Ask your agent to confirm designated agency in writing if this comes up.