Outside of Israel, many Jews, including reform, conservative and modern orthodox traditionally give their babies a Hebrew name for use in religious rituals, such as the calling up to the aliyah (benedictions) and the ketubah (marriage contract), and a secular name for purposes of civil birth records and daily use.  The mainstream and ultra orthodox as well as the chassidic Jews give their babies Hebrew and/or Yiddish names, though at times they mark the birth certificate with a secular name, to be used for purposes of civil and legal records but not for daily use.

The Hebrew name takes the form of "[child's name] bar [father's name]" for boys, or "[child's name] bat [father's name]" for girls. The name itself has no religious significance, and while it is often a Hebrew or Yiddish name, it can be a name from any language or culture. Ashkenazi Jews traditionally name their children after a recently deceased relative, a famous departed rabbi or sage, and/or biblical figures.  Sephardic Jews often name children after living grandparents as well as in honor of rabbis, famous religious figures and/or biblical figures. The following is the recitation by the father of the new born girl.

Sephardic Jews celebrate "Zeved HaBat," (Hebrew זֶבֶד הַבָּת) a ritual that has its origins in Sephardic and Italian Jewish customs dating back to the seventeenth century. The name of the ceremony derives from Genesis 30:20, preceding the birth of her daughter Dinah, Leah says; "Zevadani Elohim Oti Zeved Tov" (God has granted me a gift). The following is the recitation by the father of the new born girl in the Sephardic Community.

The words in parentheses are included in the Moroccan tradition, but not in the London tradition.

מִי שֶׁבֵּרַךְ (אִמּוֹתֵינוּ) שָׂרָה וְרִבְקָה. רָחֵל וְלֵאָה. וּמִרְיָם הַנְּבִיאָה וַאֲבִיגַיִל. וְאֶסְתֵּר הַמַּלְכָּה בַּת אֲבִיחַיִל. הוּא יְבָרֵךְ אֶת הַיַּלְדָּה הַנְּעִימָה הַזּאת. וְיִקָּרֵא שְׁמָהּ (בְּיִשְׂרָאֵל) פלונית. בְּמַזַּל טוֹב וּבְשַׁעַת בְּרָכָה. וִיגַדְּלֶהָ בִּבְרִיאוּת שָׁלוֹם וּמְנוּחָה. וִיזַכֶּה לְאָבִיהָ וּלְאִמָּהּ לִרְאוֹת בְּשִׂמְחָתָהּ וּבְחֻפָּתָהּ. בְּבָנִים זְכָרִים. עשֶׁר וְכָבוֹד. דְּשֵׁנִים וְרַעֲנַנִּים יְנוּבוּן בְּשֵׂיבָה. וְכֵן יְהִי רָצוֹן וְנאמַר אָמֵן׃

“The one Who blessed (our mothers,) Sarah and Rivkah, Rachel and Leah, and the prophet Miriam and Abigayil and Queen Esther, daughter of Abichayil — may He bless this beloved girl and let her name (in Israel) be ... [insert first name here] with good luck and in a blessed hour; and may she grow up with good health, peace and tranquility; and may her father and her mother see her joy and her wedding, and sons, riches and honour; and may they be healthy into old age; and may this be the [divine] will, and say ye, Amen!”.
 

More about Baby Girl Naming:
• Naming Ceremony: Ashkenazic Tradition
• Naming Ceremony: Sefardic Tradition, Zeved Habat
• Jewish Baby Names from A to Z