You may have noticed that in some Siddurim, the Bracha of מקדש את שמך ברבים includes G-d’s name and while in other Siddurim G-d's name is omitted. In addition, there are versions that provide שמך or שמו. Both issues represent disagreements between Ashkenazic Nuscha'Ot and Sephardic Nusacha'Ot. Here is an example of the Ashkenaz practice (סידור עבודת הלב-the new RCA Siddur):
Here is an example of the Sephardic version:
Whether you say שמך or שמו depends on how you view G-d's presence. Is it נוכח, face-to-face or נסתר, hidden or distant?
For purposes of describing one of the rules of Brachot, the focus is on whether to include G-d's name or not include G-d's name. The ב"ח
provides the answer as to why some Siddurim omit G-d's name-because the Bracha does not appear in the Talmud Bavli. Those who include G-d's name claim that the Bracha appears in the Talmud Yerushalmi. Perhaps it did originally appear in the Talmud Yerushalmi but the version that survived the Middle Ages and is in our possession does not include any reference to the Bracha.
ב"ח אורח חיים סימן מו-ומ"ש ברוך אתה יהוה מקדש את שמך ברבים. כן הוא בסדורים דמסיים בה בשם והכי משמע ממה שכתבו התוספות ריש פרק שלשה שאכלו (דף מ"ו א) בד"ה כל הברכות דמה שאינה פותחת בברוך הוא לפי שאינה אלא ברכת הודאה מכלל דמסיימת בברוך דאי אינה מסיימת לא איצטריך לטעמא למה אינה פותחת בברוך כיון דלאו ברכה היא אבל הרמב"ם לא הזכיר בה שם ונראה דסבירא ליה דכיון שלא הוזכרה ברכה זו בתלמוד בבלי אין לה דין ברכה אלא יאמרוה בלא שם ומלכות וכך ראיתי מן המדקדקים מיהו לא יורה כן לאחרים ולא ישנה הסדורים כדכתיבנא לעיל.
Translation: Concerning the Bracha of Baruch Ata Hashem Mikadesh Et Shimcha B’Rabim. So is the Bracha found in a form in which G-d’s name is mentioned. And so it seems to be the opinion of Tosafot in Brachot 46a s.v. Kol Ha’Brachot. That the reason that this Bracha does not open with the Bracha formula is that it is merely a Bracha of acknowledgement. Tosafot would not have raised this issue if the Bracha did not end with G-d’s name. Nevertheless, the Rambam does not include G-d’s name in this closing Bracha. The reason appears to be that any Bracha that is not mentioned in the Babylonian Talmud should not be treated as a Bracha but should be said without G-d’s name and hegemony. That also seems to be the opinion of those who are punctilious. But that does not have to be the rule for all. It is not necessary to change the wording found in Siddurim.
While providing the answer as to why some omit G-d's name, the ב"ח also discusses another rule of Brachot-that Brachot that express praise of G-d or acknowledgement do not have to open with a Bracha formula. It is a rule expressed by Tosafot, see the reference in the comments of the ב"ח. It is particularly important in understanding the basis on which the Talmud in bBrachot 60b provided that the first words out of our mouths as we gain consciousness each morning was the Bracha of אלהי נשמה even though it does not open with a Bracha formula. Another answer that is given concerning that issue is that the Bracha of אלהי נשמה is linked to the last Bracha recited the night before, המפיל חבלי שנה. That explains why in Nusach Provence, they began their count of the hundred Brachot a person must recite each day with the Bracha of המפיל חבלי שנה:
