By combining a Name with another, perfection upon perfection is achieved
The Beauty of the Names of Allaah, the Exalted, can be expressed through each and every Name on its own, meaning if you study Al-Hayy, you can derive many benefits. You will have much awe of Allaah and much submissiveness and humility before your Lord.
Furthermore, the beauty can be expressed by combining Names. By combining a Name with another, perfection upon perfection is achieved.
An example of that is Al-`Azeez (the All-Mighty) and Al-Hakeem (the All-Wise), since, Allaah, the Exalted, combines these Names in many places within the Qur`aan.
When used separately, each of the two Names includes a particular kind of perfection. Al-`Azeez includes `izzah (Might), and hukm (Judgment) and hikmah (Wisdom) are understood from Al-Hakeem. Allaah has Hukm; He is the Ruler and the One who legislates. And Allaah has Hikmah (All-Encompassing Wisdom).
When combined, there is another form of perfection understood – that the Might of Allaah, the Exalted, is coupled with His Wisdom. Thus, His Might does not include oppression, tyranny, and evil actions because the `izzah of Allaah is not coupled with dhulm (transgression), it is coupled with Wisdom.
The mighty ones from amongst the creation in the dunyaa may use their might for sin or to oppress people. They tend to oppress, tyrannize, and behave in evil ways.
Yet Allaah’s Might and Strength is coupled with Wisdom. So it used in a way that denotes complete Perfection.
Likewise, the Judgment and Wisdom of Allaah, the Exalted, are coupled with perfect Might and Honour, contrary to the judgment and wisdom of the Creation, as they are often subject to disgrace and humiliation.
 See the following Qur`aanic Verses for examples: Soorah al-Baqarah [2:129, 209, 220, 228, 240, 260]; Soorah Aali `Imraan [3:6, 18, 62, 126]; Soorah an-Nisaa` [4:56, 158, 165]; Soorah al-Maa’idah [5:38, 118]; Soorah al-Anfaal [8:10, 49, 63, 67]; Soorah at-Tawbah [9:40, 71]; Soorah Ibraaheem [14:4]; Soorah an-Naml [27:6]; Soorah al-`Ankaboot [29:42]; Soorah ar-Room [30:27]; Soorah Luqmaan [31:9, 27]; Soorah Sabaa` [34:27]; Soorah Faatir [35:2]; Soorah az-Zumar [39:1]; Soorah Ghaafir [40:8]; Soorah al-Jaathiyah [45:2, 37]; Soorah al-Fat-h [48: 7, 19]; Soorah al-Ahqaaf [46:2]; Soorah al-Hadeed [57:1]; Soorah al-Hashr [59: 1, 24]; Soorah al-Mumtahinah [60:5]; Soorah as-Saff [61:1]; Soorah al-Jumu’ah [62: 1]; Soorah at-Taghaabun [64:18].
Two Important Principles Concerning Allaah’s Names – Al-Qawaa’id al-Muthlaa – Istijabah.com
“All of Allaah’s Names Are Beautiful” & “They Are Both Titles And Descriptions”