From The Fabulous Fibonacci Numbers by A.S. Posamentier and I. Lehmann (Prometheus Books, New York (2007), pp. 17-18):
Leonardo Pisano - or Leonardo of Pisa, Fibonacci - his name as recorded in history, is derived from the Latin "filius Bonacci," or a son of Bonacci, but it may have been more likely derived from "de filius Bonacci," or family of Bonacci. He was born to Guglielmo (William) Bonacci and his wife in the port city of Pisa, Italy, around 1175, shortly after the start of construction of a famous bell tower, the Leaning Tower of Pisa.
The authors also indicate in a footnote that
it is unclear who first used the name Fibonacci; however, it seems to be attributed to Giovanni Gabriello Grimaldi (1757-1837) at around 1790 or to Pietro Cossali (1748-1815).
