What do we learn from "Kos Yeshu'os Esa"?
Brachos 51b: One lifts the cup of Birkas ha'Mazon a Tefach above the ground.
Rashi: I will bring Nesachim for the Korbanos Todah that I vowed, and on that cup I will call in Your name for this salvation. A Levi says Shirah only over wine (Erchin 11a).
Radak #1: Some say that Kos is portion, like "Menas Chelki v'Chosi" (16:5).
Radak #2: We can explain simply - when I will make a festive meal, I will raise a cup of wine and thank Him over it in front of many. I will mention His salvation of me. That cup is called Kos Yeshu'os.
Why does it say "uv'Shem Hashem Ekra"?
Refer to 116:4:1:1.
Radak: This is just like I did amidst affliction (verse 4).
Malbim: The primary good that Hashem saved me is not life, rather, that now I can thank Him - "Ki Tov Chasdecha me'Chayim Sefasai Yeshabechunecha" (63:4).