Customs at the Birth of a Girl

Igros Kodesh of the Rebbe, Vol. 14, p. 56, where he adds various customs in this regard see Tamei HaMinhagim, p. 396. See also Igros, Vol. 4, p. 48, note: (quoting Tamei HaMinhagim): “I have heard in the name of the tzaddik, the Rebbe of Belz, that a girl should be named after five days … but who knows if this report is true; in any case, we can only follow the instructions of our Nesi’im.” See also ibid., p. 110: “…contrary to various customs to wait several days.” See references cited in What’s in a Name?, Ch. 3. Igros, ibid., p. 48 quotes the story:…according to what my father-in-law the Rebbe related to me, that when one of the Mitteler Rebbe’s daughters was born the Alter Rebbe sent for him and said that though there is good reason supporting the custom of waiting with giving the name until the Shabbos Torah reading, nonetheless, for certain reasons, that should not be done. He then gave his daughter the name at the Torah reading closest to the birth. The fact that my father-in-law related this to me with regard to a private individual, indicates that it is an instruction for the general public.
See Likkutei Sichos, Vol. 14, p. 250; Vol. 3, p. 763ff:
A Jewish girl is regarded as one who is born circumcised (Avodah Zarah 27a), and thus her holy soul enters immediately upon birth; therefore, why should she be deprived [of her name]? See also Darkei Chayim VeShalom (customs of the tzaddik, the Rebbe of Munkacz), sect. 219.

From the text of the Rebbe’s letter sent to everyone upon the birth of a daughter.

Igros Kodesh of the Rebbe Rashab, Vol. 1, p. 210; HaYom Yom, entry for 25 Menachem Av. Cf. the text ibid., “I have heard in the name of our holy Rebbeim…”

In accordance with the dictum of the Sages (Berachos 17a), “What merit [of Torah] do women possess? [The merit of] teaching [their children] to read … [allowing their husbands] to study the Mishnah … waiting for them [to return from the cheder and beis hamedrash].