G613: It goes back to Europe as many young couples moved into the kallah’s parents house and as hakoras hatov for their support the naming went to the wife. From the chumash we see that Leah gave names to her first 4 sons, Rachel named Bilhah’s sons and Leah named Zilpah’s sons. Rachel named Yosef… וַתִּקְרָ֧א אֶת־שְׁמ֛וֹ יוֹסֵ֖ף לֵאמֹ֑ר. However, we also see that the father’s sometimes named the first born….Er, was named by Yehuda (as it says “vayikra”) וַתַּ֖הַר וַתֵּ֣לֶד בֵּ֑ן וַיִּקְרָ֥א אֶת־שְׁמ֖וֹ עֵֽר:. Yehuda’s wife named Onan as it says Vatikra וַתַּ֥הַר ע֖וֹד וַתֵּ֣לֶד בֵּ֑ן וַתִּקְרָ֥א אֶת־שְׁמ֖וֹ אוֹנָֽן: By Tamar’s twins, it says both times “Vayikra” וַיִּקְרָ֥א שְׁמ֖וֹ פָּֽרֶץ: and וַיִּקְרָ֥א שְׁמ֖וֹ זָֽרַח:. We also see that Yosef named Menashe וַיִּקְרָ֥א יוֹסֵ֛ף אֶת־שֵׁ֥ם הַבְּכ֖וֹר מְנַשֶּׁ֑ה. Moshe Rabbeinu named Gershom וַתֵּ֣לֶד בֵּ֔ן וַיִּקְרָ֥א אֶת־שְׁמ֖וֹ גֵּֽרְשֹׁ֑ם כִּ֣י אָמַ֔ר גֵּ֣ר הָיִ֔יתִי בְּאֶ֖רֶץ נָכְרִיָּֽה:
Personally, my wife and I never divulged the name to anyone before the bris.