Arabic Root:
From the root dad-lam-lam (ض ل ل), which has the following classical Arabic connotations: to be low, base, abject, paltry, to be vile, contemptible, despicable, to be inglorious, abased, humble, to be lowly, submissive, weak, to be tractable, easy, and manageable.

The following two names in the series (i.e., Al-Mu'izz and Al-Mudhill) are closely related to the previous names. The emphasis of these attributes is on giving dominion or sovereignty to the people and/or taking it away. Imam al-Ghazali writes on Al-Mu'izz, "true dominion consists in deliverance [meaning set free] from the shame of need, the dominance of passion, and the disgrace of ignorance."

Among the disputed names:
There is no ayah which explicitly mentions the name Al-Mudhill in the Qur'an, but many describe this attribute of Allah سُبْحَٰنَهُۥ وَتَعَٰلَىٰ.

قُلِ ٱللَّهُمَّ مَـٰلِكَ ٱلْمُلْكِ تُؤْتِى ٱلْمُلْكَ مَن تَشَآءُ وَتَنزِعُ ٱلْمُلْكَ مِمَّن تَشَآءُ وَتُعِزُّ مَن تَشَآءُ وَتُذِلُّ مَن تَشَآءُ ۖ بِيَدِكَ ٱلْخَيْرُ ۖ إِنَّكَ عَلَىٰ كُلِّ شَىْءٍۢ قَدِيرٌۭ

Qulil laahumma Maalikal Mulki tu’til mulka man tashaaa’u wa tanzi’ul mulka mimman tashhaaa’u wa tu’izzu man tashaaa’u wa tuzillu man tashaaa’u biyadikal khairu innaka ‘alaa kulli shai’in Qadeer

English Translation:
"Say, 'O Allah, Owner of Sovereignty, You give sovereignty to whom You will and You take sovereignty away from whom You will. You honor whom You will and You humble whom You will. In Your hand is [all] good. Indeed, You are over all things competent."— (Qur'an 3:26)

فَأَذَاقَهُمُ ٱللَّهُ ٱلۡخِزۡيَ فِي ٱلۡحَيَوٰةِ ٱلدُّنۡيَاۖ وَلَعَذَابُ ٱلۡأٓخِرَةِ أَكۡبَرُۚ لَوۡ كَانُواْ يَعۡلَمُونَ

Fa azaaqahumul laahul khizya fil hayaatid dunyaa wa la’azaabul Aakhirati akbar; law kaanoo ya’lamoon

English Translation:
"So Allah made them taste disgrace in worldly life. But the punishment of the Hereafter is greater, if they only knew."— (Qur'an 39:26)

As we mentioned in the name Al-Khafid, Allah سُبْحَٰنَهُۥ وَتَعَٰلَىٰ humbles who He chooses. In the names leading up to this one, we've briefly covered the stories of Abu Lahab, Iblees, and Firaun and how they were debased. The next verse reminds us that on the day of judgement the hypocrites will also be among those who are humbled.

يُنَادُونَهُمۡ أَلَمۡ نَكُن مَّعَكُمۡۖ قَالُواْ بَلَىٰ وَلَٰكِنَّكُمۡ فَتَنتُمۡ أَنفُسَكُمۡ وَتَرَبَّصۡتُمۡ وَٱرۡتَبۡتُمۡ وَغَرَّتۡكُمُ ٱلۡأَمَانِيُّ حَتَّىٰ جَآءَ أَمۡرُ ٱللَّهِ وَغَرَّكُم بِٱللَّهِ ٱلۡغَرُورُ

فَٱلۡيَوۡمَ لَا يُؤۡخَذُ مِنكُمۡ فِدۡيَةٞ وَلَا مِنَ ٱلَّذِينَ كَفَرُواْۚ مَأۡوَىٰكُمُ ٱلنَّارُۖ هِيَ مَوۡلَىٰكُمۡۖ وَبِئۡسَ ٱلۡمَصِيرُ

Yunaadoonahum alam nakum ma’akum qaaloo balaa wa laakinnakum fatantum anfusakum wa tarabbastum wartabtum wa gharratkumul amaaniyyu hatta jaaa’a amrul laahi wa gharrakum billaahil gharoor Fal Yawma laa yu’khazu minkum fidyatunw wa laa minal lazeena kafaroo; ma’waakumun Naaru hiya maw laakum wa bi’sal maseer

English Translation:
"The hypocrites will call to the believers, “Were we not with you?” They will say, “Yes, but you afflicted yourselves and awaited [misfortune for us] and doubted, and wishful thinking deluded you until there came the command of Allah. And the Deceiver deceived you concerning Allah. So today no ransom will be taken from you or from those who disbelieved. Your refuge is the Fire. It is most worthy of you, and wretched is the destination."— (Qur'an 57:14-15)

Reflection:
As mentioned in Al-Mu'izz - To be among the honored Allah سُبْحَٰنَهُۥ وَتَعَٰلَىٰ tells in Surah Hujurat verse 76, "O mankind, indeed We have created you from male and female and made you peoples and tribes that you may know one another. Indeed, the most noble of you in the sight of Allah is the most righteous of you. Indeed, Allah is Knowing and Acquainted."

This famous verse addresses racial discrimination and prejudice. We are all created from male and female (understood to mean our origin is the same as Adam and Eve). Allah سُبْحَٰنَهُۥ وَتَعَٰلَىٰ has created us to meet other tribes so that we may get to know one another. To gain knowledge and to further understand the human condition. Despite the visible differences, we bleed the same. In the commentary of Tafhim ul-Quran, "O people, be aware: your God is One. No Arab has any superiority over a non-Arab, and no non-Arab any superiority over an Arab, and no white one has any superiority over a black one, and no black one any superiority over a white one, except on the basis of taqwa (piety)." With this in mind, one can characterize themselves by this name of Allah سُبْحَٰنَهُۥ وَتَعَٰلَىٰ by using their strength and might to what has been commanded and to uphold/honor it. The opposite for Al-Mudhill is also true. To lower and debase that which Allah سُبْحَٰنَهُۥ وَتَعَٰلَىٰ has forbiden.