The name Saul is is the New Testament in 21 verses, 24 times.
All but one of the verses is about the disciple. Acts 13:21; is about Saul of the old Testament.
The name Paul is in the New Testament 165 times, in 160 verses.
They are all about disciple "Paul".
Did Paul go to a legal court and have his named changed legally? Unlikely, such things were not required nor done in those days.
However I do notice that Paul starts off all letters the same way...
Rom 1:1; Paul, a bond-servant of Christ Jesus, called as an apostle, set apart for the gospel of God,
1Cor 1:1; Paul, called as an apostle of Jesus Christ by the will of God, and Sosthenes our brother,
2Cor 1:1; Paul, an apostle of Christ Jesus by the will of God, and Timothy our brother, To the church of God which is at Corinth with all the saints who are throughout Achaia:
Gal 1:1; Paul, an apostle (not sent from men nor through the agency of man, but through Jesus Christ and God the Father, who raised Him from the dead),
Eph 1:1; Paul, an apostle of Christ Jesus by the will of God, To the saints who are at Ephesus and who are faithful in Christ Jesus:
Php 1:1; Paul and Timothy, bond-servants of Christ Jesus, To all the saints in Christ Jesus who are in Philippi, including the overseers and deacons:
Col 1:1; Paul, an apostle of Jesus Christ by the will of God, and Timothy our brother,
1Thes 1:1; Paul and Silvanus and Timothy, To the church of the Thessalonians in God the Father and the Lord Jesus Christ: Grace to you and peace.
2Thes 1:1; Paul and Silvanus and Timothy, To the church of the Thessalonians in God our Father and the Lord Jesus Christ:
1Tim 1:1; Paul, an apostle of Christ Jesus according to the commandment of God our Savior, and of Christ Jesus, who is our hope,
2Tim 1:1; Paul, an apostle of Christ Jesus by the will of God, according to the promise of life in Christ Jesus,
Tit 1:1; Paul, a bond-servant of God and an apostle of Jesus Christ, for the faith of those chosen of God and the knowledge of the truth which is according to godliness,
Phm 1:1; Paul, a prisoner of Christ Jesus, and Timothy our brother, To Philemon our beloved brother and fellow worker,
I wonder why Paul would identify himself as "Paul" in all of these letters. The Greek word here is...
G3972
Παῦλος
Paulos
pow'-los
Of Latin origin; (little; but remotely from a derivative of G3973, meaning the same); Paulus, the name of a Roman and of an apostle: - Paul, Paulus.
Total KJV occurrences: 163
2Cor 10:1; Now I, Paul, myself urge you by the meekness and gentleness of Christ—I who am meek when face to face with you, but bold toward you when absent!
Gal 5:2; Behold I, Paul, say to you that if you receive circumcision, Christ will be of no benefit to you.
Eph 3:1; For this reason I, Paul, the prisoner of Christ Jesus for the sake of you Gentiles—
Col 1:23; if indeed you continue in the faith firmly established and steadfast, and not moved away from the hope of the gospel that you have heard, which was proclaimed in all creation under heaven, and of which I, Paul, was made a minister.
Col 4:18; I, Paul, write this greeting with my own hand. Remember my imprisonment. Grace be with you.
1Thes 2:18; For we wanted to come to you—I, Paul, more than once—and yet Satan hindered us.
2Thes 3:17; I, Paul, write this greeting with my own hand, and this is a distinguishing mark in every letter; this is the way I write.
Phm 1:19; I, Paul, am writing this with my own hand, I will repay it (not to mention to you that you owe to me even your own self as well).
In all the verses above, Paul identifies himself as "I, Paul" (myself - Paul). So while Paul may or may not have legally changed his name.
He certainly identified himself as Paul after being converted. This was a common practice in the Bible
Abram to Abraham, Jacob to Israel, etc...
