His full name was simply "Pythagoras."
He was always reffered to as Pythagoras of Samos.
Firstly in Greek, then in English.Ὁ Πυθαγόρας ὁ Σάμιος or simply Ὁ Πυθαγόρας; Pythagoras of Samos or Pythagoras the Samian, Or Pythagoras Patel
His only name in historical record is Pythagoras, he is sometimes called Pythagoras of Samos
Pythagoras's mother's name was Pythais.
The name for the followers of Pythagoras was the Pythagoreans.
He was simply known as Pythagoras of Samos.
No one knows.
Her name was Pythais.