These answers are correct, but one thing we commonly do in GA is have the closing attorney's office simply go ahead and draw up the deed with your wife's name on it and you can go ahead and sign it at closing. The attorney's office will simply have you sign the original one in your name and then immediately sign the 2nd one. They will record them both the same day. This eliminates the need for you to have to wait or go down to the courthouse and do it yourself. They usually don't charge for that here, unless it's a simple fee for recording it. Good luck!
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And what's so important about that; what's the urgency?
You can add her after it is RECORDED, by simply going down to the County Recorders Office and asking them.
Congratulations on both.
Good luck and may God bless