🔼The name Felix in the Bible
There is only one man named Felix in the Bible. Marcus Antonius Felix (dubbed Claudius Felix by Josephus; for more on Josephus, see our article on Dalmanutha) was the Roman procurator of Judea (52 to 58 AD) who dealt with the apostle Paul as he began his tour of the Roman legal system.
Angry Jews had dragged Paul out of the temple of YHWH in Jerusalem and were about to lynch him when he was rescued by a Roman commander named Claudius Lyssias (Acts 23:26), who brought him to the military barracks (Acts 21:30-33). After letting Paul address the crowd and noticing that this didn't have the desired pacifying effect, the commander decided to flog Paul, whereupon Paul informed the man that he was a Roman citizen and could not be flogged (22:25). The commander released him but ordered him to be heard by the Sanhedrin (22:30). Paul managed to divide the Sanhedrin's opinion (23:9) to such as degree that they decided to have him assassinated (23:12). Word of that reached the commander, who promptly sent Paul to Felix in Caesarea under heavy guard (23:24).
Governor Felix was a Greek freedman, who had risen to power thanks to his esteemed older brother Marcus Antonius Pallas, who worked for emperor Claudius. Despite the salving words of prosecutor Tertullus (24:2), Felix' cruelty and corruption had increased the unrest in Judea (24:26). Apparently, Felix possessed detailed knowledge of Paul's theology (called The Way: Acts 24:22, see Acts 9:2, 19:9, 19:23, 24:14, a nickname possibly coined by Jesus, see John 14:6, who possibly had drawn it from texts like Isaiah 26:7-8, 35:8 and 40:3; see Matthew 3:3), but that didn't change his behavior much. Felix was married three times, twice to a lady named Drusilla. Wife number two was Drusilla, daughter of Herod Agrippa (Acts 24:24), whose final claim to fame was that she died in the eruption of Mount Vesuvius (along with her son Marcus and Pliny the Elder).
The name Felix occurs 9 times in the New Testament; see full concordance.
🔼Etymology of the name Felix
The name Felix is the same as the popular Latin adjective felix, which literally means fruit-bearing, fruitful or fertile (of trees or lands), and as such it's comparable to Hebrew names like Ephraim and Ephrathah. The adjective felix comes from a root feo, fevo, meaning to bear or produce, and is cognate with the Greek verb φυω (phuo; Luke 8:6, Hebrews 12:15).
The adjective felix, however, is mostly used in the sense of fruitfully, abundantly or (more) successfully, and as such came to mean lucky, happy or fortunate, and as such, the name Felix can be compared with the Hebrew names Asher and Gad.
The name Felix has been popular for a very long time. An early Roman dictator Lucius Cornelius Sulla attained the agnomen Felix later in life, as the Latin interpretation of a Greek nickname he had acquired earlier: Επαφροδιτος, Epaphroditus, which also occurs as a Biblical name (Philippians 2:25, 4:18). Certain Christian denominations venerate a dozen-and-a-half or so saints named Felix. There were three popes named Felix and two antipopes (known as Felix I through V, because in the roaring early days of the church it was often unclear who was the proper pope and who the opposing antipope.)
The name Felix literally means Fruitful, but in the sense of Happy With A Lot, simply Fortunate or Lucky.