The Disapprover, The Inflictor of Retribution, The Retaliator.
Allah سُبْحَٰنَهُۥ وَتَعَٰلَىٰ is Al-Muntaqim (in Arabic: ٱلْمُنْتَقِمُ), The One who victoriously prevails over His enemies and punishes them for their sins. Allah is most patient, but the time will come when justice must be given. Avoid things which Allah سُبْحَٰنَهُۥ وَتَعَٰلَىٰ has forbidden, for He is swift and just with His punishment and does not let trespassing go unaccounted for.
From the root nun-qaf-mim (ن ق م), which has the following classical Arabic connotations: to dislike, disapprove, find fault, to punish, exact vengeance, to inflict retribution, avenge.
From The Story of Prophet Nuh (as):
The story of Prophet Nuh (as) is very illustrative of this name. We briefly mentioned how Prophet Nuh (as) preached for 950 years, "And We certainly sent Noah to his people, and he remained among them a thousand years minus fifty years, and the flood seized them while they were wrongdoers" (Qur'an 29:14) The people denied His message, which was one thing, but that rejection turned into harassment, and they slowly grew hostile towards him.
The Qur'an even mentions possible death threats Nuh (as) had to endure, "They said, 'If you do not desist, O Noah, you will surely be of those who are stoned.'" (Qur'an 26:116) and also, "The people of Noah denied before them, and they denied Our servant and said, 'A madman,' and he was repelled." (Qur'an 54:9). Some Qur'an interpreters mention that stoning may not be literal but refer to constant abuse, slander, or vilification from all sides. This is the view of early Qur'an exegetes with regards to the phrase "al-shaytan al-rajim" as literally meaning "the stoned shaitan" but now more commonly as "the accursed satan." This symbolizes a metaphorical stoning rather than a literal one. Regardless, after centuries of calling people to embrace Islam but it falling on deaf ears and patiently enduring the abuse, Nuh (as) cried out to his Lord with this supplication
Rabbigh fir lee wa liwaa lidaiya wa liman dakhala baitiya mu’minanw wa lil mu’mineena wal mu’minaati wa laa tazidiz zaalimeena illaa tabaaraa
"My Lord, forgive me and my parents and whoever enters my house a believer and the believing men and believing women. And do not increase the wrongdoers except in destruction." — (Qur'an 71:28)
In Surah al-Qamar we also learn of the exact du'a Nuh (as) made before the flood:
Fada’aa Rabbahooo annee maghloobun fantasir
"So he invoked his Lord, 'Indeed, I am overpowered, so help.'" — (Qur'an 54:10)
And so what proceeded was retributive justice, "Then We opened the gates of the heaven with rain pouring down" (Qur'an 54:11). The same fate is mentioned of Firawn, "So We took retribution from them, and We drowned them in the sea because they denied Our signs and were heedless of them." (Qur'an 7:136). In every example, you will find that Allah's punishment is not without cause. He is the impartial judge (Al-Hakam. He gives repeated signs of His mercy and allows for the perpetrator to return back to Him (the virtue of also being At-Tawwab). If they decide to remain defiant, defensive, and thankless, then inevitably, they will pay the price.
From the story of Nuh (as), we also learn that his son was among those who drowned. He refused to accept Allah سُبْحَٰنَهُۥ وَتَعَٰلَىٰ and even on the day when the storm came, he told his father he rather goes to the top of the hill than with him on the boat. "[But] he said, 'I will take refuge on a mountain to protect me from the water.' [Noah] said, 'There is no protector today from the decree of Allah, except for whom He gives mercy.' And the waves came between them, and he was among the drowned." (Qur'an 11:34)
This is a hard but an important lesson. Despite the Prophets (may peace be upon them) being favored by Allah سُبْحَٰنَهُۥ وَتَعَٰلَىٰ to spread His message, there is no favoritism. Every person will be held accountable for their actions. It does not matter what lineage or bloodline a person comes from. These things may matter in the realm of human politicking, but in receiving Allah's mercy or punishment, it holds no precedence. Every person will be held responsible for what they earn.
Fa immaa nazhabanna bika fa innaa minhum muntaqimoon
"And whether [or not] We take you away [in death], indeed, We will take retribution upon them." — (Qur'an 43:41)
Yawma nabtishul batsha tal kubraa innaa muntaqimoon
"The Day We will strike with the greatest assault, indeed, We will take retribution." — (Qur'an 44:16)
Min qablu hudal linnaasi wa anzalal Furqaan; innallazeena kafaroo bi Aayaatil laahi lahum ‘azaabun shadeed; wallaahu azeezun zun tiqaam
"Before, as guidance for the people. And He revealed the Qur’an. Indeed, those who disbelieve in the verses of Allah will have a severe punishment, and Allah is exalted in Might, the Owner of Retribution." — (Qur'an 3:4)
This name is important to understand for several reasons. The first is to instill fear. This can remind those in power that they are still accountable to Allah سُبْحَٰنَهُۥ وَتَعَٰلَىٰ. He punishes those who cause disharmony, oppress, and tyrannizes His creation.
It teaches us at the individual level that we will be held accountable for whatever good or bad we do. It provides assurance and peace to victims of abuse that their perpetrator will face the most just of judges. He has complete knowledge and knows the appropriate action to handle each situation.
In Imam al-Ghazali's book, he writes the best vengeance is on the enemies of Allah سُبْحَٰنَهُۥ وَتَعَٰلَىٰ, but the worst of all the enemies is one's lower soul. "As it is reported regarding Abu Yazīd - may God be merciful to him that he said: 'My soul was so lazy one night as to keep me from a litany, so I punished it by depriving it of water for a year." So take vengeance against oneself in matters where one lets down. In failing to be obedient in worship, in giving, in showing kindness, in repressing anger, in controlling one's tongue. Each person has their own struggle, and in this way, they should pursue the path of vengeance.