The name Saliba is derived from the Holy Crusades of the Middle Ages. Literally translated, Saliba means "the Cross" or "the Crusader".
During the Middle Ages, Christian Europe, especially as it pertained to the Catholic Church, grew more and more vexed by the Muslim occupation of the Holy Land, ie., the area of the middle east that is known today as Israel and Lebanon.
A confederation of European nation-states, at the behest of the Pope, assembled an army to travel to the Holy Land and liberate it from the hands of what was considered the infidel Arabs. These Crusades lasted several hundred years.
Many of the Knights and warriors that traveled the long, overland distances from Europe to the Holy Land, did not wish to return home after the wars were over.
They stayed, took wives of local descent, and made their new homes in the Christian colonies of the Holy Land.
Naturally, the Saliba family is Christian, not Muslim, and tends to practice the Eastern Orthodox version of Catholicism (although my family is traditionally western Roman Catholic).
The Saliba ancestry is most prevelant in the mountainous, northern region of Lebanon, centered around the town of Beit Adin. From there, one can stand atop snow-capped mountains, dense with the lush, cedar forests that are the symbol of the county's flag, and gaze at the deep blue of the Mediterranean, sparkling below.