The name Habakkuk means primarily to embrace. It comes from the Hebrew verb ḥābaq (חָבַק), meaning "to embrace," with the form ḥăḇaqqūq likely indicating an ardent or repeated embrace.
This meaning was the original Hebrew verb. It did not change due to the book. But the prophet who penned it got his name from the verb with that meaning. (Many people in the Bible get meaningful names like this. For example, Joshua means "God saves", David means "beloved", Isaac means "he laughs", Sarah means "princess", etc.)
We can see from the Bible why the prophet was named this, because he repeatedly embraced God (spiritually speaking) despite the vision he saw.
Habakkuk was given a vision of the destruction of his people. That is, the Chaldeans (Babylonians) would invade Israel. The prophecy was fulfilled around 600 BC.
When Habakkuk saw the vision, instead of getting angry at God, he said:
"Are You not from everlasting,
O Lord, my God, my Holy One?
We will not die.
You, O Lord, have appointed them to judge;
And You, O Rock, have established them to correct.
Your eyes are too pure to approve evil,
And You can not look on wickedness with favor." (Habakkuk 1:12-13)
Habakkuk's close relationship with God is evident when he used the phrases "my God" and "my Holy One". He also understood that God appointed the Babylonians to judge his people who were sinning against Him.
However, Habakkuk still had some deep, pressing questions:
1. Why does God allow a more lawless people to judge those who are more innocent than they? (Habakkuk 1:13)
2. What will happen to the evildoers who rampage the earth to kill and capture? (Habakkuk 1:15-17)
So Habakkuk humbly stood on his guard post to watch what God would say. He expected to be corrected (reproved) but asked anyway (Habakkuk 2:1).
God answered:
"Behold, as for the proud one,
His soul is not right within him;
But the righteous will live by his faith." (Habakkuk 2:4)
God said the righteous will live by believing and having faith in God. This is the basis of the gospel of salvation through Jesus later on.
But the prideful one will suffer downfall. Utter disgrace will come upon evildoers (Habakkuk 2:16) and the enemy of the Lord will die (Habakkuk 3:13).
"Woe to him who builds a city with bloodshed
And founds a town with violence!
Is it not indeed from the Lord of hosts
That peoples toil for fire,
And nations grow weary for nothing?
For the earth will be filled
With the knowledge of the glory of the Lord,
As the waters cover the sea." (Habakkuk 2:12-14)
All nations are guilty of sinning against God. Therefore, judgement will come around to all nations. But in the end the knowledge of God and His glory will fill the earth.
However, Habakkuk also understood that what was prophesied must take place and he could do nothing to save his own people.
"I heard and my inward parts trembled,
At the sound my lips quivered.
Decay enters my bones,
And in my place I tremble.
Because I must wait quietly for the day of distress,
For the people to arise who will invade us." (Habakkuk 3:16)
Nevertheless, Habakkuk continually embraced God. He had a spirit of faith and courage, and he loved the Lord despite these judgements, because he believed in God's salvation.
"Though the fig tree should not blossom
And there be no fruit on the vines,
Though the yield of the olive should fail
And the fields produce no food,
Though the flock should be cut off from the fold
And there be no cattle in the stalls,
Yet I will exult in the Lord,
I will rejoice in the God of my salvation." (Habakkuk 3:17-18)
So Habakkuk means to ardently embrace God.
No, the identity of the writer is known. His name is Habakkuk.
His name is in the book twice:
"The oracle which Habakkuk the prophet saw." (Habakkuk 1:1)
"A prayer of Habakkuk the prophet, according to Shigionoth." (Habakkuk 3:1).
The name Habakkuk means to embrace ardently.
God, through His foreknowledge of the prophet, caused him to be named this way.
We can say that Habakkuk lived up to his name.
That is one way to understand this.
However, the more accurate way is that God knows everything beforehand and He knew what His word (the Bible) should say.
God raised up prophets through whom He would say those words.
God raised up prophets by creating them, naming them (directly or indirectly through their parents), and guiding them to know Him.
Finally, God spoke through the prophets and they wrote down His words in each book of the Bible.
The books of the Bible convey what God wants to say to us. Some of the books are named after the prophets, who lived up to their names by God's grace and help.
As a caveat to us, it may be easier for us readers to identify the books' message through the prophets' names.
However, the main message of the Bible is through the words in the Bible. (The prophets' names might be a side message or detail.) But the meat of God's word and what He wants to convey to us is in the words of the Bible.