There are various explanations of the origins of the Sabatini name, which is extremely common in Italy--the name fills more than two pages of the Rome phone book and is common throughout Italy. The most ancient reference to the name is found in the writings of Cicero, who in the third century BC wrote about the people of Italy of that time. In his Italia tributim descripta, SABATINA is the name of one of the 17 original tribes within the Roman dominion of that time. The SABATINA tribe occupied various areas in northern and central Italy (see map).
Just north of Rome are the Sabatini Mountains--remnant of the ancient toponomy--while the nearby Lake Bracciano was known as Lacus Sabatinus in Roman times.
Another explanation for the name Sabatini is given by Emidio De Felice in his Dizionario dei Cognomi Italiani (A Dictionary of Italian Surnames). He claims that it is derived from Sabato--the name given to children born on Sabato (saturday). But this seems an unlikely explanation--since it would follow that there would be just as many people named after the other days of the week; except for Domenico--named after the Saint--few Italian families, if any, have a surname derived from the other weekdays.
A third derivation, brought recently to my attention, has to do with the fact that in the past the sabatinis were barbers that worked only on Saturdays, and followed other trades the rest of the week. At one time, most men shaved only once a week--on Saturdays--for the weekend. This usage has come back into fashion in Italy-- but now sabatini are those that grow a beard all week and wait for the weekend to shave.