Why was the name "Allah" preceded by the definite article "al-," and why was the alif omitted from "Alhamdulillah" and not written in the Qur'an despite its presence?

Scholars have differed regarding the word of majesty "Allah": is it murtajal (underived) or mushtaqq (derived)? One group holds that it is murtajal, meaning it is not derived from anything else, but rather is a proper noun for the Lord of Might. This is the Greatest Name, described by all attributes, and no one else is named by it. Another group holds that it is mushtaqq, and they differed concerning its root derivation. It was said: from "laha yaleeh," meaning "he rose high"; and it was said: from "laha yalooh," meaning "he became veiled"; and it was said: from "alif-lam-ha" (أله) with meanings of worship, tranquility, bewilderment, and fright. As for the alif and lam (ال) in it, if it is said to be murtajal, then they are original; and if it is said to be mushtaqq, then they are extra. The questioner is advised not to delve into doubts and respond to them until they have achieved scientific and spiritual mastery, in order to protect the religion and Muslims.