Fibonocci was not his original name. His name is Leonardo Bonnocci. He got his nickname Fibonocci after his death in 1240-1250. No one knows for sure when though.
How Leonardo found out the Sequence: While he was in North Africa going to school, he figured out the Sequence after learning the golden ratio from the Egypt. Then taking it to Italy.
Over time we still see the repetitive golden ratio and the number sequence in many historical monuments, that some believe aliens had to do with. And if you look hard enough you can see it all around you.