Why are the connotations of this Pasuk? Why did Yisrael insert it in the Shirah?
Rashi #1 & #2: Refer to 15:7:3:1 & 2.
Ramban #1: Yisrael Davened that, having demonstrated that He is the absolute ruler, by saving His servants and destroying those who rebelled against Him, Hashem should continue to govern forever, to watch over the Tzadikim and punish the Resha'im. 1
Ramban #2 (citing Targum Onkelos): Hashem's Kingdom lasts forever. 2
Rashbam: After Yisrael have settled in Eretz Yisrael, may Hashem's Kingdom become known throughout the world.
Seforno: Once Yisrael have built the Beis-ha'Mikdash, may Hashem rule forever, "and may no other 'god' be with Him". 3
Targum Yonasan: 'When Yisrael, the erstwhile exiles, witnessed the miracles and wonders of the Yam-Suf and the might of His Hand - they said to one another to place a crown of greatness upon the Head of their Savior, who removes but cannot be moved, who changes but cannot be changed, to whom the crown of sovereignty rightly belongs. He is the King of Kings in this world and kingship is His in the world to come ... '.
We find many Pesukim which convey similar sentiments - such as the well-known Pesukim in Tehilim "Yimloch Hashem le'Olam ... " (146:10) and "Y'hi Shem Hashem Mevorach me'Atah ve'ad Olam" (113:2 [Ramban]).
The Ramban attributes Onkelos' switching the future tense to the present to his fear of ascribing physicality to Hashem, since the future implies that Hashem will rule later, but that He doesn't rule now. In fact, it is similar in content to the Pasuk in Ashrei "Malchuscha Malchus Kol Olamim". See why he nevertheless objects to Onkelos' translation, due to many similar Pesukim that are written in the future (such as the Pasuk in Tehilim 72:19) "Veyimalei Chevodo es Kol ha'Aretz".