The newly elected pope can choose to use his birth name or he may choose to use a regnal name.
Yes, he is not required to change his name.
The pope chooses his name or may even wish to keep his birth name. It is not required for him to choose a new name.
The pope, upon election, chooses his regnal name. He is not required to do so and may keep his birth name if he so chooses.
There is no list of names. A pope can choose any name he wishes and even keep his birth name.
The Black Pope's birth name is Shelly Pope.
Since Pope Francis is the first and only pope by that name, there is no need for a number after his name. If a pope in the future also decides to take the name Francis, he will become Pope Francis II and then the original Pope Francis will become Pope Francis I.
Eddie Pope's birth name is George Edward Pope.
Pope Urban chose the name upon his election as pope.
Dennis Pope's birth name is Dennis Allen Pope.
Edwin Pope's birth name is John Edwin Pope.
Everett Pope's birth name is Everett Parker Pope.
Katherine Pope's birth name is Katherine Collins Pope.