The Origin of the Name and Its Meaning

The Rebbe often interpreted the names of his predecessors, as well as the names of his family members, such as his wife Rebbetzin Chaya Mushka, his brother Reb Yisrael Aryeh Leib, and others.

The name Menachem Mendel first appears in the annals of Chabad-Lubavitch history on Sunday, 29 Elul 5549, when a son was born to Rabbi Shalom Shachne Altschuler and his wife, Rebbetzin Devorah Leah, the daughter of the Alter Rebbe, Rabbi Schneur Zalman of Liadi. At his Bris, the newborn was named Menachem Mendel in memory of his illustrious grandfather's teacher and mentor, Rabbi Menachem Mendel of Vitebsk. When he was only three years old, on 3 Tishrei, Tzom Gedalya 5553, his mother passed away. Fulfilling her final wish, the Alter Rebbe brought the young Menachem Mendel into his home and lovingly raised him, and he grew up to be the third Rebbe of Chabad, known as the Tzemach Tzedek,

The name Menachem appears in Torah and Jewish history several times:

1) Menachem ben Gadi ruled over the Kingdom of Israel, as described in Melachim II, chapter 16: "In the thirty-ninth year of Azariah the king of Judah, Menachem the son of Gadi reigned over Israel, ten years in Shomron.”
2) Menachem was the name of a Mishnaic Sage who lived in the last generation in the era of the Zugot, when Jewish leadership consisted of "pairs."  He was the "pair" of Hillel the Elder and served under him as Av Bet Din, Chief Justice of the Sanhedrin.
3) Menachem ben Yaakov Ibn Saruq was a sage and linguist who lived in Spain during the Golden Age. He is often quoted in Rashi's commentary on the Torah.

The name Mendel was common in Europe, especially among Ashkenazic Jews. In Yiddish, Mandel (a close form of Mendel) means 'almond'. Mendel also served as a surname, and was often a nickname for individuals with the name Menachem.

The Rebbe noted several times that his middle name, Mendel, is spelled with the letter Ayin, being that he is named after the Tzemach Tzedek:
 
"It is appropriate that when writing my name, it should be spelled with the letter Ayin."
 
"I have long asked the Secretariat to advise that the name Mendel is spelled with an Ayin as explained in books of Jewish names, and especially taking into account that this was the custom of the Tzemach Tzedek (which is the numerical value of Menachem Mendel [with an Ayin.]) This will surely be corrected."
 
The Rebbe also noted that Mendel is spelled without a Yud:

"Normally, the Tzemach Tzedek would sign only his first name, but in those places where he did sign with both names, his second name is spelled without a Yud."