5) The Ben Ish Chai (Year 2 Shoftim 27) maintains that even if the father wishes to forgo the honor and wishes to let the wife name the first baby after the mother’s side, he may not do so. However, Rav Ovadia Yosef zt”l writes that if the paternal grandfather is willing to forgo the honor, they may name the baby after the maternal grandfather. Such as the maternal grandfather was a rabbi etc. This is especially so when the need to maintain shalom bayis is at play. For practical halacha, a competent rabbi should be consulted.
1) The right to name the child belongs to the parents of the child and to them alone. No other person (grandparents etc.) should get involved in the naming of the child. As the Lubavitcher Rebbe zt”l writes, “As for her question regarding a suggestion as to what to name the child that was born, may he live. The Response of my father in law, the Rebbe, on this matter is known: He does not get involved in these matters. [This lack of involvement] is understood in light of the Arizal’s words that parents are given the thought from Above as to what to name the boy or girl that is born, a name connected to this child’s soul, so that the letters of the name are connected to the life force of the sould and body.” (Likkutei Sichos vol. 12 page 182. See also Bris Avos 8:30)
2) The common custom is that the parents do not reveal the name to others until the baby is formally named (the boy at the bris and there are various custom when the girl is formally named). Rav Sarya Deblitzky shlit”a explains that the reason that the name is not revealed to others is out of concern of ayin hara. (See Avnei Yashfei 1:196:6)
3) Whose side of the family should name the first child, and any subsequent children, is dependent on custom:
Sephardic Custom– The Sephardic custom has always been to name the first child from the father’s side of the family and the next child from the mother’s side and it continues with this pattern.
Rav Ovadia Yosef zt”l (Yabia Omer 5 Y.D. 21), citing Rishonim, points to the naming of Yehuda’s children in Sefer Breishis as the source of this custom. The Torah records that Yehuda named his first son (Er), and his wife named the second son (Onan). Thus it is evident that the first child is named by the father and the second by the mother. [Although, the Torah mentions that his wife named the third son as well, the Daas Zekeinim Mibaalei Hatosafos points out that the Torah specifically tells us that Yehuda was out of town at the time of the naming of his third child and was therefore unable to name him. If both parents are present, however, it seems that they should alternate namign the children, with the father naming the first child.]
4) Interestingly, the Lubavitcher Rebbe zt”l was asked what is the proper order for naming children and he explains that if there is no set custom in the locale, one should follow the custom of the Rishonim, cited above, that the first child is named by the father, the second by the mother and so on. (Likkutei Sichos vol. 7 page 308)
6) According to this custom if the child is given two names, one after the father’s side and one after the mother’s side, the name after the father’s side should be used first.
7) Ashkenazic Custom– The current Ashkenazic custom is that the mother’s side of the family has the rights to the first name. (See Hamaor 5732:2, Shearim Metzuyanim B’Halacha 163:22 and Igros Moshe Y.D. 3:101)
One reason given for this custom is that the bond between a daughter and her parents is weakened by her marriage because she leaves their home and now has responsibilities to her husband. Indeed, this weakened bond manifests itself in the halacha that a married woman is no longer obligated in the mitzvah of kibud av v’em as it may interfere with her responsibilities toward her husband. In order to strengthen this newly weakened bond, the first child is named from the mother’s side of the family. (See Kovetz Noam vol. 13 page 194)
Rav Chaim Kanievsky shlit”a offers a second reason for this custom. He explains that since the mother just went through a painful delivery process, she is given the rights of the naming of the first child in order to help ease the pain. (Halichos Ketanim U’ketanos page 31)
8) According to this custom if the child is given two names, one after the father’s side and one after the mother’s side, the name after the mother’s side should be used first.
9) Despite the various customs, cited over the last few emails, great should be taken that no arguments arise when naming the baby and that both the husband and wife are happy with the decision. (See Tziporan Shamir 186 and Ziv Hasheimos page 30)