Why did the writer of Hebrews included Hebrews 13:8? What's it for?

Hebrews 13:8 says: "Jesus Christ is the same yesterday, today, and forever." 

Yes, it is true that the Lord Jesus Christ is immutable in His nature, but the point of Hebrews 13:8 is to establish the readers in grace, in the person and priesthood of the Lord Jesus Christ. The best way to understand Hebrews 13:8 is to understand it in the overall point of the book of Hebrews. 

Heb 5:6 As He also says in another place: "You are a priest forever According to the order of Melchizedek";

 Heb 6:20 where the forerunner has entered for us, even Jesus, having become High Priest forever according to the order of Melchizedek.

 Heb 7:17 For He testifies: "You are a priest forever According to the order of Melchizedek."

 Heb 7:21 (for they have become priests without an oath, but He with an oath by Him who said to Him: "The LORD has sworn And will not relent, 'You are a priest forever According to the order of Melchizedek'"),

The Hebrews were tempted to go back to the law and the temple worship with all the priests under law. Apparently, they were tempted to think that Christ's priesthood was something like that of the priesthood under the law --- it passes from one person to another since they were prevented by death to live on and continue their ministry. 

They don't need other priests. Christ is the priest that lives on forever and ever to intercede for them. He is the same priest that they need yesterday, the same priest that they need today and the same priest they will be needing tomorrow and forever. 

Heb 7:25 Therefore He is also able to save to the uttermost those who come to God through Him, since He always lives to make intercession for them.

What Is God's Name?

 A lot of people are hung-up on what the name of God is. They import our modern way of naming certain people back to the question. In most cases, people's names in our day have no particular relevance in terms of revealing what the person is. Our names have no connection to who and what we are.

It is not so in the Bible and it is not so especially with God. In the Bible, when God reveals His name He is actually revealing something about Himself. Names are supposedly for revealing the person bearing the name. When God reveals His name or names, He is letting you know something about Himself. Nagpa-ilaila Siya nimo!

When He says that He is Elohim, He is Elohim because He is the Strong One. Elohim means the Strong One.

When He says that He is Yahweh, He is Yahweh because He is the Self-Existent One or The One Who Causes Things To Be. Yahweh means the Self-Existent One or The One Who Causes Things To Be.

When He says that He is Adonai, He is Adonai because He is the Sovereign Master. Adonai means Sovereign Master.

Some people do not approve of translating God's name in Hebrew into English because they feel and believe that if that is done then God's name would be distorted. Well, when God revealed His name His intention was to reveal who and what He is. If the English translation exactly and accurately reflects who and what He is then there is no problem.

If you translate Elohim in English as The Strong One then that's who and what God is! The Strong One. You now know in English who He is to a degree!

If you translate Yahweh in English as The Self-Existent One or The One Who Causes Things To Be then that's who and what God is! The Self-Existent One or The One Who Causes Things To Be. You now know in English who and what He is to a degree! The point is revelation. If in Hebrew you can reveal to someone who and what God is then go for it. If it is best to do it in English then go for it.

The names of God He revealed in Hebrew have relevant ideas as to who and what God is. He reveals who and what He is through His names because He wants us to adjust our lives accordingly to what He says about Himself.

"No one ascended to heaven per John 3:13?" Then What About Elijah?

 Joh 3:13 And no man hath ascended up to heaven, but he that came down from heaven, even the Son of man which is in heaven.

His Authority And His Ability

* First of all, His Authority

Why is the Lord Jesus an authority when it comes to the topic of heavenly things? (John 3 verse 12)

No one is like Him. He alone was the One who ascended to heaven and came back here to earth to tell us about it. All the prophets in the Old Testament never ascended to heaven and got their revelation there. It was God from heaven who told them about it here on earth. But not the Lord Jesus. This implies that the Lord Jesus had been ascending to heaven and descending to earth before His Incarnation. The theophanies in the Old Testament, the appearances of God in the Old Testament, was actually the Second Person of the Trinity appearing to certain people here on earth.

* Secondly, His Ability

He ASCENDED to heaven. Elijah did not ascend to heaven but was TAKEN UP there.

2Ki 2:1 And it came to pass, when the LORD was about to TAKE UP Elijah into heaven by a whirlwind, that Elijah went with Elisha from Gilgal.

2Ki 2:11 Then it happened, as they continued on and talked, that suddenly a chariot of fire appeared with horses of fire, and separated the two of them; and Elijah WENT UP BY A WHIRLWIND into heaven. No man ASCENDED to heaven by his own power, only the Lord Jesus. He certainly can tell us about heavenly things for He had the ability to beam Himself up there and fetch revelation from God the Father.