Who gave the name, and to whom (what), and why?
Shabbos 10b: Gid'on called Hashem Shalom; this teaches that Shalom is a name of Hashem. Tosfos (10b) - he called Him Shalom, for He makes Shalom, like Targum Yonasan says. 1
Rashi: Gid'on called the Mizbe'ach Hashem Shalom, for Hashem is our Shalom. 2
Malbim: Hashem called the Mizbe'ach Shalom, because the people of the city were idolaters, and they destroyed the second Mizbe'ach. This one was not destroyed, and exists until today.
Targum Yonasan says that he served on the Mizbe'ach to Hashem, who made Shalom for him. It does not discuss giving the name!
Malbim: Hashem is the thread on which all parts of the world are tied; he combines and sustains them. This is why he is called 'the King that Shalom is His.' Lev Yitzchak - Rashi explains like R. Acha (Megilah 18a), who prefers to say that the verse discusses the Mizbe'ach's name, just like "va'Yikra Lo Kel Elokei Yisrael" (Bereishis 33:20); the verse implies unlike this.
