Allah is not a name or concept of God in the bible, and Yahwah is not in the Koran. It is simple as that.
The Arabic Bible has always had 'Allah' in place of 'God'
[Qu'ran 1:1 - English translation]
"In the Name of God, the Compassionate, the Merciful."
[Qur'ân 1:1 - Arabic transliteration]
"Bismi-Allahi ar-Rahmani, ar-Raheem"
[Genesis 1:1 - English Bible - King James Version]
"In the beginning God created the Heaven and the Earth . . . "
[Genesis 1:1 - Arabic transliteration]
"Fee al-badi' khalaqa Allahu as-Samaawaat wa al-Ard . . . "
Aramaic was the spoken language of Jesus. It is a near certainty that Jesus used the word Alaha in reference to God, as well as Elohim.
"Jesus, an Aramaic speaker, would naturally use Alaha just as Aramaic speakers do today. It is simply the Aramaic version of the identical Arabic word Allah. “The cognate Aramaic term appears in the Aramaic version of the New Testament, called the Peshitta, as one of the words Jesus used to refer to God, e.g., in the sixth Beatitude, ‘Blessed are the pure in heart for they shall see Alaha.’ The Arabic Bible uses the same word in Matt. 5:8, for instance, translated Allah.” [19]"
[19] “Allah,” Wikipedia, 2005, http://www.answers.com/topic/allah, Dec. 9, 2005.
http://www.adeadlymisunderstanding.com/2010/05/is-allah-the-god-of-the-bible-pt-2/