Girls:[1]

Naming by first Keiras Hatorah-Chabad custom: The Chabad custom[2], based on a directive of the Alter Rebbe[3], Rebbe Rayatz[4] and Rebbe[5], is to be particular to name a daughter at the first opportunity, which is at the first available Kerias Hatorah [i.e. Monday, Thursday, Shabbos, Shabbos afternoon by Mincha, fast day, Yom Tov, Rosh Chodesh, Chanukah, Purim, etc etc, whichever comes first].[6] This is likewise the custom of other sects of Jewry.[7] If only this custom would become widespread amongst all Jewry, as being particular in this matter is connected with hastening the final redemption.[8] [Thus, if the child was born on Shabbos afternoon, if possible, the name should be given by Shabbos Mincha.[9]]

Other customs:[10] There are those who delay naming the daughter until the Shabbos after the birth.[11] Others delay naming the child until five days after birth.[12]

Not to use the name until the official naming of the child:[13] Whatever the case of when one names the child, even if one already decided on a name, one should not call the child by the name until the actual naming.

Prior to birth:[14] Prior to the birth of the child, one is not discuss with others the planned name of the child. [However, the parents may discuss it amongst themselves].

[1] See Igros Kodesh 4:48; 20:226; 22:260; Likkutei Sichos 14 p. 250; Toras Menachem 5750 Vol. 3 p. 364; See Shulchan Menachem 5 p. 158-159, Shaareiy Halacha Uminhag 3 p. 297; Darkei Chaim Veshalom 219 in name of Bnei Yissachar; Ziv Hasheimos 1:5-6; Toras Hayoeldes 60:7

[2] Sefer Haminhagim p. 15; Igros Kodesh 22:260

[3] Igros Kodesh 4:48, brought in Likkutei Sichos 12:182

[4] Igros Kodesh 4:48; Likkutei Sichos 14 p. 250

[5] All sources ibid

[6] The source for the Chabad custom: This was the directive of the Alter Rebbe to his son, the Mittler Rebbe, upon the birth of one of his daughters, in which he stated at that although there is reason to hold off the naming of a daughter until the Torah reading of Shabbos, nonetheless, there are greater and more overpowering reasons not to delay the naming, and to rather name the daughter on the first day in which the Torah is read after the birth. This story was related by the Rebbe Rayatz and is a public directive for all. [Igros Kodesh 4:48]

The reason: As the name of an individual is the life force and divine energy of the individual. [Now, just as we name a boy immediately upon circumcising him, so too] we should name a daughter immediately upon her being born as the sages state that a girl is considered as if she is already circumcised [Avoda Zara 27a; Derisha Y.D. 360], and it is obvious that the intent of this statement applies immediately upon birth. [Igros Kodesh 20:226; 22:260; See Sefer Ziv Hasheimos 3 footnote 15] From a different angle, from the fact that it states that the G-dly soul enters into the body of a boy upon his circumcision [Admur Basra end of 4; See Likkutei Sichos 3:763], we could deduce that by a girl, the soul enters the body immediately upon her birth, being that a woman is considered to be born in a circumcised state. At the very latest, the entrance of her godly soul is when she is given a name. Accordingly, we are careful to give a name to a girl as soon as possible, by the first Torah reading opportunity after birth. [Likkutei Sichos 14 p. 250; Darkei Chaim Veshalom 219 in name of Bnei Yissachar] Alternatively, the reason is because the Talmud [Yevamos 62a] states that the son of David will only arrive after all the souls are depleted from the spiritual warehouse of souls known as “Guf.” Now, the connection of the souls to the body is dependent on the letters of one’s name [and hence naming the child draws the soul down from its warehouse and is hence not be delayed]. [Toras Menachem 5750 Vol. 3 p. 364]

[7] Darkei Chaim Veshalom 219 in name of Bnei Yissachar; Maharam Brisk 2:7; Kochav Miyaakov 159; Igros Moshe E.H. 3:35; Nitei Gavriel 70:9 footnote 17 in name of many Sefarim and Gedolei Yisrael  and communities

[8] Toras Menachem 5750 Vol. 3 p. 364

The reason: As the Talmud [Yevamos 62a] states that the son of David will only arrive after all the souls are depleted from the spiritual warehouse of souls known as “Guf.” Now, the connection of the souls to the body is dependent on the letters of one’s name [and hence naming the child draws the soul down from its warehouse and is hence not be delayed]. [Toras Menachem 5750 Vol. 3 p. 364]

[9] See Nitei Gavriel 70:10

[10] See Nitei Gavriel 70:8-9 footnote 13 and 16

[11] Zichoron Yosef O.C. 10; Daas Torah 282; Minchas Yitzchak 4:107; Mishneh Halachos 3:321; See Igros Kodesh 4:48 in name of Alter Rebbe; Nitei Gavriel 70:9 footnote 16 in name of many Sefarim and communities and Gedolei Yisrael

[12] Sefer Taamei Haminhagim 4:75 in name of Maharash Belz [The Rebbe questions the authenticity of this statement and concludes that whatever the case, we must follow the directive of our Rabbeim]; See Nitei Gavriel 70:11 footnote 19 in name of many Sefarim and communities

[13] Shut Hamaor 1:2134; Mivaser Tov 79; Chesed Leavraham Azulai Mayan 2 Nehar 52; Ziv Hasheimos 2; Shevach Habris 21:1

[14] See Shut Hamaor 1:2134; Mivaser Tov 79; Chesed Leavraham Azulai Mayan 2 Nehar 52; Ziv Hasheimos 2; Chemdas Tzevi 5:42; Shevach Habris 20:1; Nitei Gavriel 71:1