While you may be more comfortable in using the name God(swt) over Allaah(swt), that does not mean they are 2 separate deities. There is but one God(swt) and all those of the true Abrahamic, Monotheistic, Faiths (Jew, Sabian, Christian and Muslim) worship the same One. We do argue and differ about how we worship and do disagree often over the nature of Allaah(swt) but we do understand that there is One true God(swt) and it is the same God(swt) revealed through all of the True Prophets(PBUT).
Possibly you do worship the American created God who appeared in the 1860s in the minds of Pentecostals and Fundamentalist, Bible based, self proclaimed Evangelists and Ministers. If that is your case I will agree with you that you do not Worship Allaah(swt)
What makes you think the English speaking God of Fundamental/Pentecostal Americans is the True god? The God(swt) that began appearing in America during the 1860s and rapidly spreading into over 23,000 denominations does not seem to be the same God(swt) worshiped by Jesus(as). America has Americanized God and created a Bible based series of religions that adhere to new interpretations that satisfy the individual Pastors/Ministers/etc of the newly formed denominations.
Fortunately there is still hope for most of the world's Christians as they do recognize that Allaah(swt) and God(swt) are the same and that all the True Abrahamic faiths do worship the same God(swt). Perhaps one day they will accept the Qur'an.
I worship and serve, and will not deny, the God of the Bible. This is He who created the heavens and the earth and all that is in them. This is He who called Abram and led him out of his country and took him to a land that He would show him. To him the true God gave the covenant of circumcision. From him came Isaac and Jacob, and from Jacob the 12 patriarchs. And God's promise and covenant was with Isaac and Jacob (Israel).
I worship He who delivered Joseph out of his oppression when his brothers sold him into slavery out envy and jeoulsy because God's promise was to him and not to his brothers. I worship Him who spoke to Moses from the burning bush in the wilderness of Sinai who spoke to Him saying, "I am the God of thy fathers, the God of Abraham, and the God of Isaac, and the God of Jacob."
This God led His people out of bondage to Egypt by an outstretched arm with great power and signs which He did before the all the people.
This God has spoken in times past and in various ways by the mouth of His prophets, has in these last days glorified His Son Jesus Christ, who was delieverd up and crucified, but God raised Him from the dead. The prophets foretold the coming and sufferings of Christ, and the glory that would follow. All this God has fulfilled. And now He commands all men everywhere to turn from their sin and to believe on the Lord Jesus Christ that you might receive the forgiveness of sins and everlasting life in His Name. For there is no other name given among men by which we must be saved but the name of Jesus.
All of the prophets have foretold these things, and this promise is not only to Israel, but as to as many who would call upon the name of the Lord, to the Jew first, and also to the Gentile. By Him, Jesus, all that believe are justified from all things, from which we could not be justified by the Law of Moses. We also should take a clear warning from the prophets who said, "Behold, ye despisers, and wonder, and perish: for I work a work in your days, a work which ye shall in no wise believe, though a man declare it unto you."
This is whom I serve and worship.