The question has often arisen among Christians, particularly Western Christians as to whether or not the name Allah can be used to refer to God as a Christian. I think there is a lot of misunderstanding about who Allah is and what He represents in the various faiths. I aim to get rid of a lot of misconceptions in this post and even touch on the use of the name Isa (Jesus) being used as well.
Yes and No. In reality, the God of Christianity stands out as the most unique in that He provided a definite way of salvation through Jesus Christ. Muslims and Jews do not unknowingly worship a different god. They have one god in their respective belief systems. What they do worship is one god, however. What they deny is salvation through Jesus Christ, the only begotten Son of God. That is where the controversy lies with both Judaism and Islam.
A lot of the attributes of God as listed in Islam are similar to the attributes of God in Christianity. God is love, patient, kind, merciful, judging, etc. The Muslims deny God as Father, but we can affirm together nearly every attribute that the Muslim acknowledges. Some of the concepts might be different, such as different concepts of God being love, but we can acknowledge that the names are the same. So, where's the controversy?
It lies in the origins of the name Allah. Allah is short for al-ilah which simply means the god (Phil Parshall, The Cross and the Crescent, p. 30). This is essential in showing that there is no other god before or after Allah. He is the one god. So, can a Muslim background believer still call God, Allah, after conversion? I would say yes and here's why. The meaning has changed. All these years, one has been "worshiping" an impersonal god named Allah. You can only hope for salvation once you die, but there is no hope. All of a sudden, you have come to realize that Allah did have a son named Jesus Christ who died for your sins so that you can be saved. Yes, I did use the same name. You see, the meaning has changed. I would ask the naysayers what name they would use for God for a Muslim background believer in an Arab context? Is there one? Not that I can find. Arabic Christians and Jews used the name Allah before Muhammad came around and began introducing the Allah of Islam. One can find it in literature predating Muhammad. What about the supposed idea that Allah was a moon god and that Muhammad picked one god as the supreme being? While that is possible, there is no evidence to suggest this. All the "research" done on this has only been done with the presupposition that this is what happened. In short, there is nothing wrong with using the name of Allah as long as we are clear on meaning that it is the God of the Bible and not the impersonal god of the Muslims.
There is also a charge that one should not use the name of Isa when referring to Jesus. This is really kind of silly, if you ask me, and just nitpicky. This controversy came up back in February when Rick Warren invoked the name of Isa in his prayer at the Presidential inauguration. Frankly, I'm disgusted at the attitudes that many Christians displayed with regards to this non-issue. Muslims understand the name of Isa to refer to Jesus. The Qur'an even refers to Jesus as the Messiah at times (Surah 3:38-48). I've actually learned something here. Apparently Arab Christians use the name "Yasu," a derivative of the Hebrew, "Yeshua," to refer to Jesus. Now, I don't know about you, but every Arab Christian I met in my travels in Jordan, Israel/Palestine, and Egypt used the name Isa with the exception that they added "al Masi" on the end, meaning, Jesus the Messiah. The Muslims will just use Isa. By added "the Messiah," one is indicating that they are a Christian. This seems pretty clear. Now, maybe Yasu is used by some Christians, but I never heard it once and a Muslim is not going to have a clue as to what you are talking about. The American Christian's hatred of Muslims becomes clear when one has to look into deeper meanings expressed by one's Christian prayer. Warren was already under attack for accepting the opportunity to pray anyway. He used the Hebrew name of Jesus, Yeshua, in his prayer too, but no one called him to account for that. The Jews don't believe in Jesus. They despise Him. Even the Muslims honor Jesus more than the Jews. Yet, when it comes to things of Islam versus things of Judaism, the Christians always side with the Jews. God is not a god of partiality, but desires people from every tribe and nation to worship Him. This includes both Jews and Muslims. We cannot continue to get lost in playing semantic name games. Let's just tell them the Gospel, that Jesus died and rose again so that they might have life eternally if they believe (have faith).