It was actually important to me to be around for the Kiddush, to be able to celebrate that with my family/friends/community… but I agree: NOT right after birth. My first daughter’s was soon after, because we went to the apartment my parents were renting for their stay and they arranged the entire thing. But for my second daughter we waited until she was about three months old, and I had time to recuperate, prepare for the Kiddush and be up to hosting and enjoying. It was really nice.
And sharing the meaning of the name, as you mentioned @charlesneuman, and your wishes for your daughter’s future can make it very meaningful and special.