The Supreme One wins over everyone through His qualities. He wins the affection of His devotees through His qualities of sausheelya and saulabhya. He defeats His enemies. So one way or the other, He conquers everyone who comes into contact with Him during His avataras. Some become devoted to Him; others oppose Him and are destroyed. That is why the Krishna Yajur Veda describes the Supreme One as Sakumsrushtajith, said V.S. Karunakarachariar, in a discourse.
In the Vishnu Sahasranama, one of the names of Lord Narayana is Purujith. Sankara Bhagavadpada interprets this to mean He who is successful against many. Parasara Bhattar also gives a similar interpretation. Purujith is the 508th sacred name of the Lord. Parasara Bhattar points to a sloka in the Ayodhya Kanda, 12th sarga, to justify his interpretation of Purujith as a reference to Rama. Through His honesty, He wins the hearts of people. Through His generosity, He earns the gratitude of the poor. Through His service, He impresses learned elders. As a warrior He conquers enemies. That is why He is Purujith. That Purujith (Rama) is praised by the Veda as Sakumsrushtajith.
The Supreme One is Somapaa, and this too can be appreciated in the context of the Rama avatara. When Rama performed many Asvamedha yagas, He showed the world how soma rasa should be consumed in accordance with Vedic prescriptions. Soma also means nectar, and this meaning is even more appropriate while referring to Rama, for did not Rama consume a priceless nectar? That nectar was His own story sung by His sons Lava and Kusa. What can be sweeter than His story? Valmiki, the Gopikas, and Pareekshit, had all compared narrations of the Lord’s story to nectar. So Rama, who listened to His story, is the One exalted by the Veda as Somapaa.