Most likely because the Christians and Jews that the prophet Muhammad knew in the 7th century did not use the name. Although, as you say correctly, the name Jehovah is part of the theophoric names that do appear in the Qur'an, such as Yahya and Ilyas (John and Elijah in English).
The Arabic Bible does contain God's name, as Yahwah and Yahuwah, depending on the version.
Why do people keep repeating the irrelevant quibble that "Jehovah" is not Hebrew? No one says that it is. Rather, "Jehovah" is the form of YHWH that has come down historically in English and other languages. People whose language is English use the "j" for all of the names in the Hebrew Bible that begin with "y," including John, Jesus, and others.
Further, not all scholars agree that the form "Jehovah" or "Yehowah" arose as a misreading of YHWH with the vowels of adonai ("lord"). For one thing, the vowels of Jehovah are not the same as those of adonai. For another, the form "Jehovah" or "Yehowah" can be seen in the way that the ancient Jewish historian Josephus said that the name was pronounced. "Yahweh," on the other hand, depends on ancient Greek pronunciations, not on any existing Hebrew text.
The cessation in pronouncing God's name is not mandated by the Bible, but purely by rabbinic tradition. The Bible itself is clear that God's name was freely used and pronounced by God's servants in ancient times. And it is illogical to assume that God would put His name in the Bible nearly 7,000 distinct times if He did not want it to be pronounced.
The HOLY Bible