Mountain; of the mountain
Monterrio is a modern American elaboration of the Spanish word 'monte', meaning mountain. It likely evolved as a rhythmic variant of names like Monterio or Montero, which were originally occupational surnames for people who worked on mountains or in forests.
Less common today
Monterrio isn't in the latest US Top 1000. It last peaked at #5,773 in 1991.
US births per 5-year period, 1990βpresent (SSA data).