Muslims tend to regard Paul as the person who corrupted Christianity and usually reject the epistles of Paul as authoritative scripture. Many Muslims have charged that Paul's original name was Saul (of Tarsus), and that he changed his name to Paul after his conversion, and that he had never met Jesus. Though that name change theory is relatively popular, it isn't probably what happened. Saul was a Jew AND a Roman citizen, and thus would have two names. Saul was his Hebrew name and Paulus was his Latin name. The first reports about him in the Bible are when he is in Israel and neighboring countries and there he certainly uses his Hebrew name. Later on in his missionary travels in Asia minor and Europe, he uses his Latin name, which is perfectly in harmony with his status and the places he visited. Moreover, since Paulus means "the little one", he might have seen it to be more appropriate and humble as he became a Christian instead of a name after King Saul.
And he did meet Jesus. He saw him in a vision on his way to Damascus. He might not have met Jesus while Jesus walked on this earth, but he met him after his resurrection, where he saw and heard Jesus in this incident.
Interestingly, the Muslim at-Tabari said, "Among the apostles and those disciples around them, whom Jesus sent out, there were Peter and his companion Paul." (A history of the Christian Church, Thalabii. Qisas al-Anbiyaa, pp. 389-90. Tabarii. Taarikh al-umam wa-l-muluuk II/II, 1560).
This is how Paul saw himself:
For what I received I passed on to you as of first importance: that Christ died for our sins according to the Scriptures, that he was buried, that he was raised on the third day according to the Scriptures, and that he appeared to Peter, and then to the Twelve. After that, he appeared to more than five hundred of the brothers at the same time, most of whom are still living, though some have fallen asleep. Then he appeared to James, then to all the apostles, and last of all he appeared to me also, as to one abnormally born. For I am the least of the apostles and do not even deserve to be called an apostle, because I persecuted the church of God. But by the grace of God I am what I am, and his grace to me was not without effect. No, I worked harder than all of them--yet not I, but the grace of God that was with me. Whether, then, it was I or they, this is what we preach, and this is what you believed. (1 Corinthians 15:3-11)Recommended Reading: