The eternal purpose of God is to build God into man and man into God.
This requires redemption and also transformation in the divine life.
For Jesus to change the name of Simon to Peter means that he, Peter, as representative of all the believers, must undergo a transformation in Christ's life and a building up into a corporate living house.
God's house which is the church and consummates in the New Jerusalem, is composed of God-men. The chief cornerstone of this eternal dwelling place is Jesus Christ Who was God / Man by incarnation and resurrection.
The other stones of this house are God-men by Christ's full salvation. So when Peter says "YOU ALSO"
he is actually speaking of "also" to the cornerstone Jesus Christ the original God-man.
Now look at the passage again and see that this is right.
"Coming to Him, a living stone, rejected by men but with God chosen and precious.
You yourselves also, as living stones, are [edited] being built up as a spiritual house ..."
Jesus Christ as God and man mingled, is the cornerstone, even though rejected by the religionists who persecuted Him. All the saved as "also"
to be living stones not by incarnation but by salvation, including redemption, regeneration, sanctification, transformation, conformation, building up together in love, glorification, and transfiguration in resurrection.
are to be God-men via Christ's salvation. He is the cornerstone of this building of God and man united in a blended corporate expression.