As far as I can tell, How Wright usually the following terms to explain the event of being accepted by God.
a. “Paul discovered, at the heart of his missionary practice, that when he announced the lordship of Jesus Christ, the sovereignty of King Jesus, this very announcement was the means by which the living God reached out with his love and changed the hearts and lives of men and women, forming them into a community of love across traditional barriers, liberating them from the paganism which had held them captive, enabling them to become, for the first time, the truly human beings they were meant to be. The gospel, Paul would have said, is not just about God’s saving people. It is God’s power at work to save people” (WSPRS, 61; cf. 45).
b. “Paul’s conception of how people are drawn into salvation starts with the preaching of the gospel, continues with the work of the Spirit in and through that preaching, and the effect of the Spirit’s work on the hearts of the hearers, and concludes with the coming to birth of faith, and entry into the family through baptism” (WSPRS, 125).
a. “The point of God’s covenant with Abraham, to give him a single great family, always was that this was how sins would be forgiven, and the initial establishment of that covenant embodied the same principle” (Justification, 221).
b. “…all those who believe in ‘the God who raised Jesus our Lord from the dead’ are part of Abraham’s single family, which means that they, too, have their sins forgiven” (Justification, 222).
Wright says that the “general trend, at least since the sixteenth century,” is “to make ‘conversion’ and ‘justification’ more or less coterminous,” with “conversion” taken to mean “the establishment of a personal relationship with God” and “justification” as meaning “this personal relationship between the believer and God.”
Wright intends to decouple justification from conversion, so perhaps conversion would be a suitable term for him as well. This seems right, as Wright goes on to describe the “moment of conversion, when someone who hasn’t before believed the gospel is gripped by the word and the Spirit and comes to believe it, to submit to Jesus as the risen Lord” (http://www.ntwrightpage.com/Wright_New_Perspectives.pdf).