[according to the Ramchal in Adir BaMurom, this might (the possibility is based only on my weak memory) signify the conquering of the Kav - the Beam of the Ayn Sof - over the Chalal, which is very reminiscent of what Rabbainu says (LKM 64) that the song of the Tzadik fixes the heresy in the Chalal.]
The gimatriah, numerical value, of Avram Avraham is exactly Na Nach Nachma Nachman MeUman (also the name Avrhaham, starts with Alef (1), Beis (2), showing the progression, and also the remain letters Resh and Mem have the numerical value of the acronym of Na Nach Nachma Nachman MeUman - 240)!
Afterwards H"Y changed our Mother's name Sara, from Suray to Sarah.
Rabbi Nachman wrote in LK"M (Torah 49:5) that Sarah represents the revelation of the song which is Single, Double, Triple, Quadruple.
It is possible to say that here we find a hint, that first there is the revelation of the actual song (lyrics), while the tune is still hidden, as Suray is in the possessive tense, only afterwards is the tune revealed to the whole world, Sarah.
Later Sarah gives birth to Isaac - Yitzchak (will laugh), upon giving birth to Yitzchok, Sara said whoever hears will laugh, i.e. whoever hears Sara, the song that is Single, Double, Triple, Squared, will laugh. This is the holy laughter we hear from Saba Yisroel.