How are we changed in regeneration?
We are made partakers of the divine nature and experience newness of life.
Catechism for the Global Methodist Church, question 62
6And he was faithful in the LORD, and he reckoned it to him as righteousness.
5Your name shall no longer be called Abram, but your name shall be Abraham, for I have made you the father of a multitude of nations.
10God said to him, Your name is Jacob; you shall no longer be called Jacob, but Israel shall be your name. So he called his name Israel.
3Jesus answered and said to him, "Truly, truly, I say to you, unless one is begotten from above, that one cannot see the kingdom of God."
1Therefore there is now no condemnation for those in Christ Jesus.
17So if anyone is in Christ, a new creation: the ancient things have passed by; look, new things have come to be.
22The fruit of the Spirit is love, joy, peace, patience, kindness, goodness, faithfulness. 23Gentleness, self-control; against such things there is no law. 24Those who belong to Christ Jesus have crucified the flesh with its passions and desires.
2Set your minds on the things above, not on the things upon the earth. 3For you have died, and your life is hidden with the Christ in God.
3As his divine power has granted to us all things that pertain to life and piety through the knowledge of the one who called us by his own glory and virtue. 4Through which the precious and very great promises have been granted to us, so that through them you may become participants in the divine nature, having escaped the corruption that is in the world by desire.
4You are from God, little children, and you have overcome them, because the one who is in you is greater than the one who is in the world.

This question asks the catechism to describe the change that regeneration makes. The answer quotes Article IX of the Confession of Faith, which says that by regeneration "we are made partakers of the divine nature and experience newness of life." Both phrases are biblical. The first comes from 2 Peter 1:4, and the second is Paul's language for the life that follows baptism into Christ's death and resurrection. ΒΆ102.6 of the Book of Doctrines and Discipline places this new birth at the start of sanctifying grace, the point where God's work in a person begins to reshape the person.
The Genesis references set the pattern. Abram is told, "your name shall be Abraham, for I have made you the father of a multitude of nations" (Genesis 17:5), and Jacob hears, "Israel shall be your name" (Genesis 35:10). A new name in scripture marks a new identity given by God. Jesus tells Nicodemus that this is what entering the kingdom requires: "unless one is begotten from above, that one cannot see the kingdom of God" (John 3:3). Paul states the result without qualification: "if anyone is in Christ, a new creation: the ancient things have passed by; look, new things have come to be" (2 Corinthians 5:17).
"Partakers of the divine nature" needs a careful reading. Peter says that through God's "precious and very great promises" believers "may become participants in the divine nature, having escaped the corruption that is in the world by desire" (2 Peter 1:4). The phrase describes a creature sharing by grace in God's own holiness and life; the distinction between Creator and creature that Article I of the Confession of Faith maintains stays firmly in place. The evidence of that sharing is the fruit Paul lists, "love, joy, peace, patience, kindness, goodness, faithfulness, gentleness, self-control" (Galatians 5:22-23), and John's confidence that "the one who is in you is greater than the one who is in the world" (1 John 4:4).
Newness of life shows itself in where a person's attention rests. "Set your minds on the things above," Paul writes, "for you have died, and your life is hidden with the Christ in God" (Colossians 3:2-3). For a Methodist this is the meaning of the baptismal vows and of their renewal at confirmation: the old life has been put to death with Christ, and the new one is lived under the word of Romans 8:1, "there is now no condemnation for those in Christ Jesus."