This is an Italian or French residential surname, which originates from a place called Tremontine in France or Tremonte in Italy. Many, perhaps the majority of all surnames are locational, these surnames are now often regard as originally implying ownership of the place from where they came. This surname in its various spellings suggests a meaning of the three mountains, although whether that is a literal description of the place of origin, we are unable to say. Most residential type surnames are "from" names, which is to say that they were given to people after they left their original villages and moved elsewhere. It is true that "elsewhere" could be the next village only a mile away, or it could be the capital city, either way it was in the medieval period, and it often remains so today, that the easiest way to identify a stranger was to call him or her, by the name of the place from whence they came. Upto about 1890, writing and spelling being at best problematical, and local accents being very thick, often lead to the development of some unusual spellings. In this case early examples of the recordings include Maria Tremonte of Pietremonte Corvino, province of Foggia, on April 15th 1816, and Lucia Tremonti, at Castelnuovo del Fruitili, province of Udine, both Italy, on November 30th 1830.