The Great Theophany is not spelled out in Scripture as much as it is repeated in Hebrew writ.
For instance, though Abraham has personal theophanies, this is followed up by the angel visitors that both Abraham and Sarah and their servants see and wait upon. Though Moses has a personal theophany at the burning bush, he leaves with signs to show the people and wonders to work upon Egypt before the exodus leads to the Great Theophany at Sinai. All the other prophets of Jewish history either work their wonders or give their oracles in public. This pattern is that of public theophany vs. the type of hidden wonders performed by Jesus (who tells people not to spread reports of him or chooses only a few people to perform miracles in front of) or private visions like claimed by Joseph Smith of the Mormons. The tenet is not a command from Scripture but was learned by the Jews' contact with YHWH over the centuries and is one of the reasons Jesus is not acceptable as the Messiah.
Davening can be repetitive, at least the form Orthodox Jews engage in. However the Name is not repeated or used in liturgy, and Davening is an official liturgical action so there is not even use of the Name in this practice. It is also not the "babbling like the Gentiles," although Protestants who abhor Catholic forms of prayer (simply due to anti-Catholicism) tend to ignore the "like the Gentiles" part and just concentrate on forbidding all use of repetition.