Since we seem to be going in circles let's put forward several points known or explored in the academic and historical world.
Hebrew, Aramaic, and Greek were some of the languages used in the area and its surrounding region. Neither the Hebrew Bible nor the Christian New Testament were written predominantly in Aramaic, in fact the vast majority of the Text is in Hebrew or Greek. Nowhere in either the Tawrat/Torah or the entire Hebrew Bible does the word 'Allah' appears, neither does it appear in the Christian Bible or the Injil as it were.
The term Allah may be used by Arabic speaking Christians and has been translated as such into Arabic Bibles, which means they have been using the term in a monotheistic context while to pre-Islamic Arab pagans the term referred to a local South Arabian deity which was one of many, in several cases perhaps not even the most popular deity, for example the Nabateans celebrated the worship of Dushara widely. In addition it's worth looking into if the Christian term 'Allah' originated from Syriac Aramic (or even other Aramaic dialects) as opposed to the Muslim Arabic 'Allah'. The word even shows differences in etymological qualities from the Arabic term.
One major and basic thing to repeat is that Allah can be in use as a generic term for 'God'. So what does it exactly prove that other people in contemporary or historical terms use it? In addition it is interesting to note that in an ancient site I researched in Southern Israel, as the Byzantines Christianized the local population, you could still see Bishops keeping their Semitic name Abdullah, or Abd Allah=Servant of Allah, Allah being a major pagan god on the South Arabian pantheon. Several centuries before Islam or befor a pagan shrine called the Kaaba was converted into Islam's sacred ground as Muhammd tried to break Quraysh monopoly on the site by dedicating it exclusively to Allah, leaving him as sole deity in the site, removing the recognition of his daughters for example who were widely worshiped by the local population.