Sorry, Pope "Badassmotherfucker" is reserved should Samuel L. Jackson ever run for the papacy.

It's just tradition. Early popes used their own names. The tradition started in the 6th century because an elected pope was named Mercurius after the Roman god and he thought it was bad PR to keep it. The last pope to use his birth name was in the 16th century (Marcello II)

The Pope is asked what name they will use. This is after they accept the position of pope, which means they are already pope at that moment.

So they can pick whatever name they want. They aren't going to be fired.

Seriously though they don't have to pick a new name at all. It's often meant to be symbolic or recognizing a mentor or influence.

Pope Todd the first.

Usually that's a saint's name, but also popes are elected and sometimes it's a shorthand that they'll continue policies of previous pope of that name

They recycle names and add a roman numeral. Robert Francis Prevost is Pope Leo XIV.