There is no need to record a new deed unless it is important to you to do so. In general the simplest way to handle is to have the note indicate something to the effect: X corp formerly known as Y corp, by virtue of a name change filed with the Georgia Secretary of State on MM/DD/YY.
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There is a specific provision of the Georgia Nonprofit Corporations Code which answers your question. I don't know the cite offhand, but what I've done is to file a "Notice of Corporate Name" change in the real estate records and attach as an exhibit a Certified Copy of the Certificate of Name Change issued by the GA Secretary of State. For good measure, have the Ceritificate cross-referneced on the real estate records to the original deed under with the entity obtained title.
[This communication is intended as general information and not specific legal advice, and this communication does not create an attorney-client relationship.]