I'm referring to the MAX version of the Punisher. Ok, Francis "Frank" David Castiglione is his birth name then he changed his last name to Castle. When and why? 

Well don't quote me on this, but when Frank joined the police he might have changed his name to Castle to sound less Italian, which back in the day was a mark against those joining a police force because of the mafia. Again don't quote me on that, but it does sound like a good enough explination to me :)

Hehehe you have a solid point there!!

he changed his name to Castle to illegally re-enlist to do a fourth tour in Vietnam

Dude I'm referring to the MAX version of the Punisher not the 616. If you've read the Punisher: Born and the Tyger and every bits and pieces of the series, he only had THREE tours in Nam. Do you know Firebase Valley Forge? It was his third and final tour.

Frank's son's name is Francis David Castle Jr. but before it was Castiglione.

i dont like the castiglione name i prefer castle

 just seems more punisher to me