Arabic speaking christians Used the name Allah
Volumn 004, Book 055, Hadith Number 605.
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Narated By 'Aisha : The Prophet returned to Khadija while his heart was beating rapidly. She took him to Waraqa bin Naufal who was a Christian convert and used to read the Gospels in Arabic Waraqa asked (the Prophet), "What do you see?" When he told him, Waraqa said, "That is the same angel whom Allah sent to the Prophet Moses. Should I live till you receive the Divine Message, I will support you strongly."
Evidence from Quran that the name Allah used by Jews and Chrisitians
(They are) those who have been expelled from their homes in defiance of right, (for no cause) except that they say, "Our Lord is Allah." Did not Allah check one set of people by means of another there would surely have been pulled down monasteries, churches, synagogues, and mosques, in which the name of Allah is commemorated in abundant measure. Allah will certainly aid those who aid His (cause); for verily Allah is Full of Strength, Exalted in Might, (able to enforce His Will). (Quran 22:40)
Other than this you have to provide contrary proof that the Arabic speaking Christians and Jews used another name other than "Alllaah".