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.
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?