Ohr Sameach gives the chronology according to Rashi of the giving of the Torah.
Early the following morning, the 2nd of Sivan, Moshe goes up Mt. Sinai for the first time. He is instructed to offer the Jews the opportunity of accepting the Torah, and of becoming a holy people. (19:3-6). That same day Moshe descends and assembles the elders and passes on the message. The entire people respond in unison that whatever HaShem says, they will do. (19:7-8).
Beis Tefillah Yonah Avraham points out that this day
is traditionally known as Yom HaMeyuchos (loosely–the special day). Aruch haShulchan explains why: This is the day that Moshe Rabbeinu told B’nei Yisrael that they must sanctify themselves in preparation for mattan Torah.
I always thought that it had this name because we became a ממלכת כהנים וגוי קדש and that is the yichus, distinguished lineage that we have.
What sources are there for the meaning of Yom HaMeyuchos?