Saul of Tarsus, and the Apostle Paul are the same man:
ACTS 13:9 Then Saul, (who also is called Paul,) filled with the Holy Ghost, set his eyes on him,
Before Paul (Saul) was an Apostle, he was a persecuter of the Church:
ACTS 9:1 And Saul, yet breathing out threatenings and slaughter against the disciples of the Lord, went unto the high priest,
ACTS 9:2 And desired of him letters to Damascus to the synagogues, that if he found any of this way, whether they were men or women, he might bring them bound unto Jerusalem.
ACTS 9:3 And as he journeyed, he came near Damascus: and suddenly there shined round about him a light from heaven:
ACTS 9:4 And he fell to the earth, and heard a voice saying unto him, Saul, Saul, why persecutest thou me?
ACTS 9:5 And he said, Who art thou, Lord? And the Lord said, I am Jesus whom thou persecutest: it is hard for thee to kick against the pricks.
ACTS 9:6 And he trembling and astonished said, Lord, what wilt thou have me to do? And the Lord said unto him, Arise, and go into the city, and it shall be told thee what thou must do.
Paul was told what he must do by the mouth of Ananias. However, Paul was known to be a persecutor of the church. Ananias was somewhat worried about being arrested by Paul, so God (whose name is Jesus Christ) had to prepare Ananias for this meeting with Paul. God told Ananias:
ACTS 9:13 Then Ananias answered, Lord, I have heard by many of this man, how much evil he hath done to thy saints at Jerusalem:
ACTS 9:14 And here he hath authority from the chief priests to bind all that call on thy name.
ACTS 9:15 But the Lord said unto him, Go thy way: for he is a chosen vessel unto me, to bear my name before the Gentiles, and kings, and the children of Israel:
ACTS 9:16 For I will shew him how great things he must suffer for my name's sake.
As this story is told in Acts 9, this is all that Paul was told:
ACTS 9:17 And Ananias went his way, and entered into the house; and putting his hands on him said, Brother Saul, the Lord, even Jesus, that appeared unto thee in the way as thou camest, hath sent me, that thou mightest receive thy sight, and be filled with the Holy Ghost.
ACTS 9:18 And immediately there fell from his eyes as it had been scales: and he received sight forthwith, and arose, and was baptized.
Paul was told what he must do (per Acts 9:6), and Paul was baptized. This was one of the things he was told to do, as we will see later.
11.2.1 Saul (Paul) was baptized in the name of Jesus Christ. The only name mentioned in this story, is "Jesus" (Acts 9:5, Acts 9:17). Therefore, it is unreasonable to conclude that Paul was baptized with the words "In the name of the Father, and of the Son, and of the Holy Ghost." (It has been demonstrated in sections 6.0 and 6.1 that that phrase is found nowhere in the book of Acts.) It is much more reasonable to conclude that Paul was baptized in the name of "Jesus Christ," consistent with the precedent of Acts 2:38, and of the Samaritans at Acts 8:12, and of the Ethiopian eunuch at Acts 8:37-38.
11.2.2 Nowhere does it specifically say here that Saul actually believed. There are those who point that the book of Acts does not always specifically mention baptism at each example in which men are saved. It should be noted that at Acts 9, the Bible likewise does not specifically say that Paul believed either.
So the question remains: did Saul believe? Yes. How do we know this? It doesn't actually say that he believed. It is understood that Saul believed, in part because of the precedent (section 7) of earlier examples (Acts 2:41, Acts 4:4, etc.), and in part because it is consistent with what Paul himself would later write (Hebrews 11:6, etc.)
11.2.3 Paul did not speak in tongues. Ananias was sent, in part, so that Saul would be filled with the Holy Ghost (Acts 9:17). Acts 9 does not say that Paul ever "spoke with tongues." The baptism of Paul demonstrates that the Holy Ghost can be received without any "initial evidence" of speaking in tongues. Compare this with the baptism of Jesus Christ in section 1.1.2, above.
Years later, Paul addressed the Jews:
ACTS 22:7 And I fell unto the ground, and heard a voice saying unto me, Saul, Saul, why persecutest thou me?
ACTS 22:8 And I answered, Who art thou, Lord? And he said unto me, I am Jesus of Nazareth, whom thou persecutest.
ACTS 22:10 And I said, What shall I do, Lord? And the Lord said unto me, Arise, and go into Damascus; and there it shall be told thee of all things which are appointed for thee to do.
According to Paul, what was Paul told? He was told:
ACTS 22:14 And he [i.e., Ananias] said, The God of our fathers hath chosen thee, that thou shouldest know his will, and see that Just One, and shouldest hear the voice of his mouth.
ACTS 22:15 For thou shalt be his witness unto all men of what thou hast seen and heard.
(It just so happens that the Bible, from Romans thru Hebrews was written by Paul.) But Paul was also told:
ACTS 22:16 And now why tarriest thou? arise, and be baptized, and wash away thy sins, calling on the name of the Lord.
11.4.1 Baptism is to be done in the name of Jesus Christ. According to Paul's recount of his conversion, Paul was baptized in the name of Jesus Christ. The only name mentioned here is "Jesus of Nazareth, whom thou persecutest" (Acts 22:8). It is not reasonable to conclude that Paul was baptized with the words "In the name of the Father, and of the Son, and of the Holy Ghost." (It has been demonstrated in sections 6.0 and 6.1 that that phrase is found nowhere in the book of Acts. ) The only reasonable conclusion that can be reached is that Paul was baptized in some variation of the name of "Jesus Christ" (such as, "Jesus of Nazareth," for instance).
11.4.2 Baptism is for the remission (forgiveness) of sins. According to Paul, his own baptism was to "wash away [his] sins" (Acts 22:16), that is, it was for remission of sins just like Peter said in Acts 2:38 during his precedent-setting preaching:
ACTS 2:38 Then Peter said unto them, Repent, and be baptized every one of you in the name of Jesus Christ for the remission of sins, and ye shall receive the gift of the Holy Ghost.