My understanding of your question is that you are looking for the perspective of Christians who believe they worship a different deity from Muslims. So I'll give you my no. 1.
The God I serve, who is the God of the Bible, has a name, His name is Jehovah. The Lord's prayer clearly declares:
"Our Father, who is in heaven, Hallowed be thy name..."
He clearly revealed to us His name so we can use it. Inasmuch as there may be contradicting reasons as to why the name Jehovah was removed from many verses in the Bible, the consensus is that this name Jehovah was and is in the original books (taking into account tetragrammaton);
Now, from my research, I can't find the name of the deity of the Quran anywhere. And before anyone questions it, may I say Allah is not a name, it's a title? Allah is Aramaic and/or Arabic for God; Just as Dios is spanish for God. So I'm yet to hear the name of god of the Quran.
And No, I don't belong to a group or denomination; I just believe in the Bible as the inspired Word of The Living God and Jesus as His only begotten son.
Allah - https://en.wikipedia.org/wiki/Allah
Tetragrammation - https://en.wikipedia.org/wiki/Tetragrammaton
The Lord's prayer by Robert Vannoy - https://goo.gl/FpnJsu