The name for the followers of Pythagoras was the Pythagoreans.
The Pythagoreans
Both. There was a man named Pythagoras and his followers were called the Pythagoreans. Yes, there was someone called Pythagoras, and those loyal to him were Pythagoreans, though Pythagoreans sounds more like a tribe of natives than a bunch of people who followed a man.
He was simply known as Pythagoras of Samos.
Pythagoras of Samos
His only name in historical record is Pythagoras, he is sometimes called Pythagoras of Samos
Pythagoras.
Pythagoras
Pythagoras's mother's name was Pythais.
His full name was simply "Pythagoras."
Pythagoras was philosopher, mathematician and founder of a religious group
Pythagoras is not known to have had any named partners. However, he did have many disciples who followed him in philosophy, mathematics and religion. Plato and Aristotle were both influenced by Pythagoras's principles.