A couple of important and basic question: What are the explanations about why Shavuot is also called by the name “Atzeret” (where is the first time it was called it and by who?)? Does it have something to do with the completion of the Sefirat haOmer ? Or what makes Shavuot “atzeret” ? Another question: why does the Torah not mention that Ma’amad Har Sinai and the giving of the Torah took place in the holiday of Shavuot, but rather in other terms (completion of the Sefirat haOmer, the harvest of the fruits ...) ? How are these other terms connected to Ma’amad Har Sinai ... given that the best known aspect of the holiday is the Giving of the Torah! Please, I’d like to have as many explanations (if there are divergences) / sources as possible!
Atzeret literally means "the end" from the root: ATzR= "stop". Accordingly, just as Shmini Atzeret is the 8th day and end of Sukkot, already chazal (Mishna, Rosh HaShana 1, 2) in the Oral Law, refer to the end of the Pesach period after 7 weeks (not days, as in Sukkot!), with the 50th day of Atzeret, the beginning of the 8th week. All explanations of this Omer period, deal with the gradual process of spiritual independence and freedom, which sees the Pesach period as climaxing with Shavuot. The Yalkut Shimoni on Pinchas (782) explains that actually Shmini Atzeret should have also been the 8th week (and not 8th day) counting from the 1st day of Sukkot, but God didn't want to trouble us during the rainy season to come twice to Jerusalem. R. Ovadia Sforno explains that the Shavuot was "supposed to" be called Atzeret already in the Written Torah, for it also means "holy gathering" (= all "stop" their regular actions and "stop" to meet together), for that was what happened at Sinai, but when 3,000 people worshiped the Golden Calf there, and ruined the "holy gathering", that term was not used. All Torah holidays represent a national, historical and religious event, as well as an annual agricultural event. This isn't felt that much outside of the Land of Israel, where the climate and agricultural seasons may differ greatly from where the holiday was, and today- once again is, meant to be observed, in Israel. Regarding the date of the Torah giving, there is also an opinion in the Talmud (Shabbat 87b) that the Torah was given on the 7th of Sivan. Similarly, when the Sanhedrin would consecrate Rosh Chodesh through witnessing the new moon, the holiday could come out anywhere between the 5-7 of Sivan (depending if Nissan and/or Iyar were 30 days). Accordingly, the 50th day may not necessarily fall on the day the Torah was given in the original year of the exodus! The Magen Avraham (494, 1) explains that's why the holiday is called in Ya'aleh v'Yavo: "Zman Matan Toratenu"= the time/period (and not "the day"!) of the giving of our Torah, for it may not be the exact date, but it is the period of time (Pesach and Shavuot were also worded accordingly).