The name-giving of the daughter --known in Sephardic communities as Zebed haBat and in some Ashkenazi communities as Shabua haBat-- takes place usually during the first Shabbat or within the first month after the birth of a girl.
As to the ceremony, there are many different traditions. I describe the ceremony according to Siddur bene tzion (there are no talmudic sources for it).
1.The father is invited to the Torah and after he finishes his Aliya a prayer is recited:
2. Before the prayer, the Chazan or the Rabbi recites a verse from Shir haShirim (The Song of Songs 2:14) praising the pristine beauty and the sweet voice of the baby girl. If she is the first girl to be born in the family, another verse (6:9) is added, describing her as a unique beautiful creature, the new Princess of the home.
3. Then, the name is giving:
"He Who blessed our mothers Sara and Ribka, Rachel and Lea, the prophetess Miriam, Abigayil and Queen Esther, the daughter of Abichayil, may He bless this beloved girl and let her name in Am Israel be known as:... (here her Hebrew is pronounced and the name of her father: for example, "Rachel bat Abraham". In many communities they mention the name of the mother as well, i.e., Rachel bat Abraham and Sara...)... with good mazal and in a time of blessing. May she grow up with good health, peace and tranquility; and may her father and her mother merit to see her joy and her wedding, with sons, prosperity and honor; and may they be healthy and fresh, and live until an old age; and so may this be His will, and let us say, Amen!".
4. In many Sephardic communities the mother is also welcomed to say from her seat the thanksgiving blessing (Birkat haGomel) .
I dedicate today's Halakha of the Day to my new grandchild, 'Michal', the daughter of David and Keren Bitton. She was born in Shanghai, China.