Let me get this straight. The actual name of the region's Moon-god was Sin, while his mere title was al-ilah, i.e. "the god," meaning that he was the chief or high god. And your argument is that Allah cannot be God is because the title was also in use by other polytheistic religious groups, a high god in a pantheon, who were from the same region before Muhammad... and based on this we jump to a conclusion that Allah is name of a pagan god and just completely ignores that the Israelites have this EXACT issue.
Moses identified the regional Canaanite high god El with their own god even though he originally presided over a large pantheon long before the Israelites entered Caanan. AND the closely related plural form elohim is used more often in the Bible, but both derive from the same Semitic root as Allah (El-lah). Arabic being a secondary branch of Hebrew. And Canaanite being the closest language to Bible Hebrew there is, and so applying your same logic we are all pagans; OR, you're wrong, and just like the Canaanite and Hebrew words "El" and "Elohim" and "Ellah", the Arabic "Allah", and the pre-Christian, Germanic word "God", they can all refer both to the Judeo-Christian god and other supernatural beings, including foreign gods/demons in both the Bible and Quran, without such wild implications that compels you to hold such a glaring double standard.
Secondly, unless you've been formally ordained by the laying on of hands of the Christian presbytery with active authority whereby a demon might recognize your authority, calling upon the name of Jesus won't give you any ability to bind a demon.
"Jews, exorcists, took upon them to call over them which had evil spirits the name of the Lord Jesus, saying, "We adjure you by Jesus, whom Paul preacheth". And there were seven sons of one Sceva, a Jew, and chief of the priests, which did so. And the evil spirit answered and said, "Jesus I know, and Paul I know; but who are ye?" And the man in whom the evil spirit was leaped on them, and overcame them, and prevailed against them, so that they fled out of that house naked and wounded." (Acts 19:13)
