The origin of the name Felix is Greek
This is how Felix is written in Greek
Φῆλιξ = Phēlix
the meaning of the name Felix is: happy
Felix was a Roman procurator of Judea appointed by the emperor Claudius
The name Felix appears in the bible in the following verses:
And provide them beasts, that they may set Paul on, and bring him safe unto Felix the governor.
Claudius Lysias unto the most excellent governor Felix sendeth greeting.
We accept it always, and in all places, most noble Felix, with all thankfulness.
And when Felix heard these things, having more perfect knowledge of that way, he deferred them, and said, When Lysias the chief captain shall come down, I will know the uttermost of your matter.
And after certain days, when Felix came with his wife Drusilla, which was a Jewess, he sent for Paul, and heard him concerning the faith in Christ.
And as he reasoned of righteousness, temperance, and judgment to come, Felix trembled, and answered, Go thy way for this time; when I have a convenient season, I will call for thee.
But after two years Porcius Festus came into Felix’ room: and Felix, willing to shew the Jews a pleasure, left Paul bound.
And when they had been there many days, Festus declared Paul’s cause unto the king, saying, There is a certain man left in bonds by Felix: