No, Allah is an Arabic word that means God (The God) and is used by Arabic speaking Christians for The God of Abraham, Isaac, and Jacob (even before Mohammed was born and created Islam).
“Allah is an Arabic word that means God”
Allah was one of the Gods in Arab’s Pagan pantheon (the Moon God), before Mohammad raised him to the position of sole creator, that later made “Allah” synonymous with the monotheistic God of Abraham.
Muhammad’s own father, was named after the pagan god Allah (Abdullah, literally “slave of Allah”).
Their Allah never had a son.
Sura 18.4 “And warn those who say: Allah has taken a son.”
Sura 9:30 that those that believe Allah has a son should be destroyed by Allah.