According to Dr Sharib:

"Al-Muzill is the One Who puts to humiliation anyone He likes."

To emulate the Name we are advised to show respect to others, so that we
may not be put to humiliation.

Repetition under the prescribed conditions gains one protection from envy,
jealousy, and the evil designs of people. It can enable one to gain what
constitutes a right from the people.

see 'The 99 Most Beautiful Names of Allah' by Dr Zahurul Hassan Sharib

Some other references:

Al-Ghazali refers to God's way of bringing the persons who love the creatures
rather than their Creator, to the point where their greed cannot be satisfied, till
they deceive themselves and remain in ignorance and darkness.

(Al-Ghazali - The Ninety-nine Beautiful Names of God. Trans. Burrel/Daher: ITS: 1992.)

The one who seeks dominion in this world is fated to be humbled. Mevlana
Rumi points out with regard to the intellect and also to physical beauty which
can give a certain dominion:

'Beauty in humankind is like gilding; else how did your sweetheart become an
old ass.
She was like an angel, she became like a demon, for that loveliness in her was
a borrowed thing.

Little by little He takes away that beauty: little by little the sapling withers.

Go recite 'to whomso We grant length of days, him we cause to decline'. Seek
the heart, set not thy heart on bones.

The Mathnavi: Mevlana Jalaluddin Rumi Book 2 : 712-715

The poet Shelley shows the same thing, when he has the plaque on a lifeless
statue of an ancient long dead king that is dicovered in the middle of a desert,
read with a double meaning:-

"'My name is Ozymandias, king of kings, look on my works you mighty and

All around, boundless and bare the lone and level sands stretched far away."

Bismillah ir Rehman ir Rahim
The Dishonourer, The Abaser, The One Who
Humbles, The One Who Looks Down on All Things
Qur'an 3:26 (a derived Name)
Say: "O, Allah!
Lord of Power (and Rule)
Thou givest Power
To whom Thou pleasest,
And Thou strippest off Power
From whom Thou pleasest,
Thou enduest with honour
Whom Thou pleasest,
And Thou bringest low
Whom Thou pleasest:
In Thy hand is all good,
Verily, over all things
Thou hast power.
Qulillah-humma Maalikal-Mulki
tu'-til-Mulka man-tashaaa-'u wa
tan-zi-'ul- Mulka
mimman-tashaaa'. Wa tu-'izzu
man-tashaa-'u wa tuzillu
man-tashaa': bi-yadi-kal-Khayr.
'Innaka 'alaa kulli shay-'in Qadiir.

Qur'an 3:26 (trans. Y. Ali)