The Gaon says that Azazel is the name of a mountain. It is so called because of its might. God’s name is mentioned in Azazel as it is in ke-harere el (the mighty mountains) (Ps. 36:7) and in yakti’el (Joktheel) (II Kings 14:7). This is in error.
If you are able to understand the secret that follows Azazel then you will know its secret and the secret of its name, for it has comrades in Scripture. I will reveal a bit of its secret to you in a hint. When you are thirty-three, you will understand it.
If you count 33 verses you will understand why the goat was sent into the wilderness. If we count 33 verses we come to Lev. 17:7. The Torah there prohibits Israel from sacrificing to the se’irim (satyrs). According to I.E. the se’irim were demons that had the shape of goats. Weiser suggests that the goat was sent to a place of demons so that the sins which it (literally or symbolically) bore would not contaminate people, for demons dwell in a place which is uninhabited.

AND THE OTHER LOT FOR AZAZEL. It is explained more clearly in the Chapters of the great Rabbi Eliezer: “The reason why they would give Azazel [i.e., Satan] a conciliatory gift on the Day of Atonement, was so that he should not annul [the effect of] their offerings, as it is said, one lot for the Eternal, and the other lot for Azazel, the lot of the Holy One, to be a burnt-offering, and the lot of Azazel to be ‘the goat of sin,’ bearing upon it all the iniquities of Israel, as it is said, And the goat shall bear upon him all their iniquities.

When Azazel saw that he could find no sin on the Day of Atonement amongst them [the children of Israel], he said to the Holy One: ‘Master of all worlds! You have one people on earth who are comparable to the ministering angels in the heavens. Just as the ministering angels are barefooted, so are the Israelites barefooted on the Day of Atonement. Just as the ministering angels do not eat or drink, so is there no eating or drinking in Israel on the Day of Atonement. Just as the ministering angels have no joints [in their feet, and therefore cannot sit or lie down], so do the Israelites stand on their feet on the Day of Atonement. Just as there is peace in the midst of the ministering angels, so do the Israelites bring peace among themselves on the Day of Atonement. Just as the ministering angels are free from all sin, so are the Israelites free from all sin on the Day of Atonement.’ And the Holy One, blessed be He, hears the testimony concerning Israel from their prosecutor, and God atones for the altar and for the Sanctuary, and for the priests and for all the people of the assembly, as it is said, And he shall make atonement for the most holy place etc...."

Now the intention in our sending away the goat to the desert was not that it should be an offering from us to it — Heaven forbid! Rather, our intention should be to fulfill the wish of our Creator, Who commanded us to do so. This may be compared to the case of someone who makes a feast for his master, and the master commands the person making the feast, “Give one portion to that servant of mine,” in which case the host gives nothing [of his own] to that servant, and it is not to show him honor that he acts in that way to him, but everything is given to the master and it is the master that gives a gift to his servant; the host only observes his command and does in honor of the master whatever he commanded him to do. The master, however, out of his own compassion for the host, wanted all his servants to derive some enjoyment from it [the feast], in order that they may all speak of his [the host’s] praise and not of his shortcomings.
This then is the reason [for having someone] who casts the lots [on the two goats]. If the priest were to dedicate them merely, by word of mouth [without casting the lots], saying, “one for the Eternal” and “one for Azazel,” that would be like worshipping [Azazel] or taking a vow in its name. Rather, the priest set the two goats before the Eternal at the door of the Tent of Meeting, for both of them were a gift to G-d, and he gave to His servant that portion which came to him from G-d. It is he [i.e., the priest] who cast the lots on them, but it is His hand that apportioned them, something like that which it says, The lot is cast into the lap; but the whole disposing of it is of the Eternal. Even after the casting of the lots, the priest placed the two goats before the Eternal, thus proclaiming that both are His and that by sending one away [to the desert] we intend merely to fulfill G-d’s wish, just as it said, And the goat, on which the lot fell for Azazel, shall be set alive ‘before the Eternal,’ to make atonement over him, to send him away etc. That is the reason why we do not ourselves do any act of slaughtering [of that goat, as this would imply that it is a proper offering which requires slaughtering].