I have read several questions and answers on here regarding repeating words in prayer, but they do not answer why some common repetitions are allowable.
Some examples:
1) During the Torah service, it is common to repeat "Ki mi-Tziyon tetze Torah" and "Barukh she-natan Torah, Torah".
2) During Aleinu, it is common to hear "u-Shkhinat uzo, u-Shkhinat uzo" and most infamously "u'shmo, u'shmo, u'shmo ehad."
3) Possibly most problematic, in some synagogues there is a custom of singing and repeating "V'techezena ainainu b'shuvkha l'Tzion b'rachamim." during the Chazarat ha-Shatz and also of "Sim, sim, sim shalom, sim shalom tovah u'brakhah."
The answer to Repeating words in prayer makes a convincing case that unnessessary repetition was looked down on by many authorities, especially for the Chazzan.
The answer to Is repeating the chorus in Lecha Dodi problematic? makes a distinction between a piyut and a tfilla and points to the relevance of whether a name of God was used. Those criteria make sense, but by them there are problems with the minhagim listed above:
1) Since the Torah service is a davar shbikedusha (a prayer that can only be recited in the presence of a minyan) should these not be repeated?
2) Isn't "Shkhina" a name of God ("the Presence"). Also can't "u'shmo" x3 be construed as trinitarian as Jake and Josh Waxman pointed out? Ironic, in a piyut composed against idolatry.
3) It seems like these ones might be the most flagrant violations of halacha since it is in the Shemona Esrei and since "Shalom" is a name of God. Is this changed by the fact that this happens during the repetition rather than during the silent Shemona Esrai?
Am I getting carried away with what might be harmless customs or are these actual deviations from halacha?
