What is the relationship between faith in Christ and publicly confessing His name? Both go hand in hand with each other. We confess His name by faith. Confession is not a meritorious deed. Confession is not something that we attach to faith as a requirement or prerequisite for salvation. It is simply an expression of faith. The main reason for public confession was so that fellow Christians could help keep each other accountable and for the sake of honor.
Audible confession of Christ's Lordship is evidence of a changed heart, as such will certainly bring about persecution. In context, the Apostle Paul is giving particular emphasis to the simplicity of receiving the righteousness of God. Receiving His forgiveness comes by faith, not keeping the Law. We are saved because God is gracious. The object of our faith is Jesus Christ. The Apostle Paul is not hereby placing faith and confession in a sequential or chronological fashion, but resorting to a literary device called parallelism.
A faith which results in justification before God comes "from the heart." That inward faith will manifest itself with an outward declaration of "Jesus is Lord." That is brought about through the repentance of sin. A faith that reflects trust in God cannot exist apart from repentance. It is for this reason salvation cannot exist apart from the confession of Christ's Lordship. It is an inherent characteristic of a saving faith. It is the outworking of a regenerate heart.