Depends on what (or whom) is behind the rise in popularity of Monte in Armenia. If it turns out that the Armenian-American revolutionary Monte Melkonian (1957-1993) is behind it, then it actually is possible that Monte ultimately comes from Montgomery. However, we will likely never know for certain what inspired his parents to name him Monte back in the '50s.https://en.wikipedia.org/wiki/Monte_Melkonian (in English; he was born in California)By the way, the Armenian name source listed below makes no mention of the name. This possibly indicates that the name has no long and established history in Armenia, i.e. it was introduced there relatively recently.http://armenian.name/index.php?a=list&d=1&p=6&w1=M (in English)
Forchta in biuonga quamon ouer mi, in bethecoda mi thuisternussi. In ic quad: "uuie sal geuan mi fetheron also duuon, in ic fliugon sal in raston sal?"