In birchot hashacher the siddur says (edoth hamizrach):
האיש מברך בָּרוּךְ אַתָּה יְהֹוָה אֱלֹהֵינוּ מֶלֶךְ הָעוֹלָם. שֶׁלֹּא עָשַׂנִי אִשָּׁה: האשה מברכת ללא שם ומלכות בָּרוּךְ שֶׁעָשַׂנִי כִּרְצוֹנוֹ:
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That Berakha is not found in the Talmud or early authorities, and generally we do not add blessings on our own. Thus many authorities did not think it should be said (eg. Bach, Shelah, Peri Chadash (cf. Be'er Heitev OC 46 sk 8)). Leaving out the name of God is a way to avoid making this a formal Berakha.
This has nothing to do with Nusach per se, but is rather just a Halakhic question, with rabbis from all groups coming out on different sides (eg. Arukh haShulchan writes that the custom around him was not to say this blessing), and generalizing positions to whole communities based on the whims of Siddur-publishers is likely counterproductive. Best to speak with your rabbi for a final ruling.