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1. The names of the Holiday?

Shavuos: The most common used name to refer to the Holiday is the name “Shavuos”, and this is the official name used in Halachic literature.[1] This name is found in the Torah in two areas of scripture.[2] This name is due to the fact that the holiday comes after the count of the seven weeks of Sefiras Haomer, and a Shavua in Hebrew means a week, and hence we call it Shavuos. Alternatively, it hints to the pact made between the Jewish people and Hashem on Har Sinai, as the word Shavua also means swear or pact.

Chag Habikkurim: One of the names that the Holiday is referred to in the Torah is Chag Habikkurim.[3] This is because the Bikkurim [first fruits of the orchard] were only allowed to be brought to the Temple beginning from Shavuos.[4] Alternatively, this is because on Shavuos the offering of the Shtei Halechem [Two loaves] is brought to the Temple, which was the first “Bikkurim” of the public wheat offerings brought in the Temple.[5]

Chag Hakatzir: One of the names that the Holiday is referred to in the Torah is Chag Hakatzir [festival of harvest].[6] This is because the harvest began shortly prior to the Holiday of Shavuos, and on Shavuos an offering from the new grain was brought. 

Atzeres: In the wording of the Sages[7], the Holiday of Shavuos is called by the name “Atzeres”.[8] The reason behind this name is because it is the Aramaic translation of the word Shavuos.[9] Alternatively, the days between Pesach and Shavuos are similar to Chol Hamoed, and thus the Holiday of Shavuos is similar to Shemini Atzeres.[10] Alternatively, the reason behind this name is because all holidays have two aspects; the rest from performing Melacha and the performance of a specific Mitzvah which is relevant to that Holiday [i.e. Shofar/Matzah/Sukkah]. However, Shavuos only has the first aspect, of resting from doing Melacha, and does not contain any special Mitzvah relevant to that day. For this reason, it is called Atzeres which means to stop, in order to emphasize that this is its main factor.[11]

Zeman Matan Toraseinu: In the prayer of Shemoneh Esrei on Shavuos the Holiday is referred to as “Zeman Matan Toraseinu” as on this day we received the Torah. 

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[1] This name used throughout all the laws in the Shulchan Aruch chapter 494 in Michaber and Admur.

[2] Pinchas 28:26 “Shavuoseichem”; Riei 16:10 “Veasisa Chag Hashavuos”

[3] Pinchas 28:26; Emor 23:17

[4] Rambam Hilchos Bikkurim chapter 2:6

[5] Rashi in Torah Bamidbar 28:26; See Rambam Hilchos Temidim Umusafim 8:11

[6] Shemos 23:16

[7] Pesachim 68a; Rosh Hashanah 6b

[8] Admur 494:1

[9] Birkeiy Yosef 494:1; Pesikta Pinchas; Kaf Hachaim 494:4

[10] Ramban Emor 23:36

[11] Kedushas Levi Parshas Bamidbar

[12] Reshimos Devarim 1 p. 332; Otzer Minhagei Chabad p. 321