Don't worry, you'll get the hang of the "name mutation" with time...!
"Jesus" is not a common name in Anglo culture but quite popular in cultures influenced by the Spanish and Portuguese.Just think of the many Latinos in the US called "Jesus" (pronounced Hay-sus).
The name is not overly popular in Lebanon/Syria but you find it mostly in Christian communities (Catholic, Greek Orthodox, Maronites, etc.).Your ancestors were most likely Christians since they comprised the bulk of emigration from Syrian and Lebanon during the Ottoman empire.Do you know where they were from and when they arrived in the US?
But the name is also used by Moslems since Islam recognises Jesus as one of the prophets (they differ about the "son of god" stuff) and the name is present in the Koran.