Congratulations—how exciting for you! Yes, Geico does have home insurance policies, but they are through third parties. In other words, Geico acts as an intermediary between you and the actual companies offering the policies.
Because Geico is not actually issuing you the insurance, you’ll have to deal with the company that issued you the policy to file a claim or make changes. For many people, this isn’t really an issue. If you have trouble figuring out whom to contact, Geico agents can help you.