According to Dr Sharib:

Al-Mu'izz is the One Who confers honour upon whomsoever He likes.

To emulate the name you should not look down upon anyone. It implies to
be humble, free of pride, vanity and arrogance.

Appropriate invocation earns respect and esteem.

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

Some other references:

Al-Ghazali refers to this along with the Name Al-Mudhill (the Abaser). He
talks of God giving dominion to whomever He pleases - but reminds us
that true dominion is the dominion over the self, the result of which is that
from such a one God removes the veil to reveal the beauty of His
presence and enables him to take dominion over his own soul.

He says that every man who is used to facilitating the cause of honour by
his action or his speech, possesses a share in this Name.

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

The souls of the friend's of God - the true and great Awliya (saints) , are
marked by the perfect dominion granted them by God over everything
which enters their domain. Those who associate with them thus become
enabled to better dominate or manage what enters into their own souls. It
is said that only those who are called can come into the presence of
those saints.

Bismillah ir Rehman ir Rahim
The Honourer,The One Who Raises to Honour,
The Raiser to Honour
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)