And G-d spoke to Abram, saying: “… No longer shall you be called Abram. Your name shall be Abraham, for I have set you a ‘father of multitudes of nations.’ ”
Still, the letter reish in “Abram” remained in place.
Rashi on verse
Abraham’s name change, in conjunction with his circumcision and his entry into a covenant with G-d, marked a profound turning point in his life. Up until this point, the thrust of Abraham’s life was his spiritual relationship with G-d; from this point on it was to be his role as a leader of the masses, a teacher of the divine truth to the rather un-divine multitudes.
Thus the Hebrew letter hei was added to his name. “Abram” (Avram, in the Hebrew) is an acronym of av ram, which means “exalted father”; “Abraham” stands for av hamon goyim—“a father of multitudes of nations.” But according to this, his name should have been changed to “Abham”; why was the letter reish, which stood for the ram (“exalted”) in his name, left in? There is no reish in the phrase “a father of multitudes of nations.”
Often, there is a tendency for teachers and leaders to water down their message to their constituents. For myself, goes this line of thinking, I ought to indeed pursue the ultimate, ponder the most abstract truths and set the highest standards. But it is foolish to expect the same of everyone else. How can one compare the spiritual capacity of he who leads an ordinary, mundane existence to that of one who has been seeking G-d all his life? If I speak of such matters and make such demands, I will only be perceived as out of touch with reality. Indeed, the rarefied insight and pious behavior I have attained will only be made crude and debased by its communication to the masses.
Therein lies the lesson of the irremovable reish in Abraham’s name. G-d added a hei, anointing him as a leader for the hamon (“multitudes”), but left the reish of “exalted” in. For the true mark of a teacher is one who can convey the most sublime truths to the most ordinary of minds, and the true mark of a leader is one who can inspire the loftiest aspirations in the most mundane of hearts. Such a teacher and leader was Abraham, and such is the quality of leadership he bequeathed to his heirs in their role as a “light unto the nations.”
Based on an address by the Rebbe, Shabbat Lech Lecha 5744 (October 15, 1983) 
Adapted from the teachings of the Rebbe by Yanki Tauber.
 See The Return of Hagar, WIR VII No 9
 Isaiah 42:6.
 Likkutei Sichot, vol. XXV, pp. 68-69.