Paul,

Because the Pope Before him (Pope John Paul I) had died so quickly, only 21 days in office before he died, he elected to continue with the Name. When a Cardinal is Elected to the position, they can then elect to use any name as pope they want. Pius is popular as a name, so is John and Paul, after the Apostles.

Will be interesting to see who the next Pope is and what name he takes on in his official duties.

This will be the 6 Pope for me in my life time.