The Meaning of Allah’s Name al-Hakim
Question

What is the meaning of Allah’s name al-Hakim?
Praise be to Allah.First meaning of Allah’s name Al-Hakim
The name of Allah al-Hakim is of the “fa‘il” pattern which, from a grammatical point of view is an emphatic form of either:     
The “fa‘il” pattern, in which case hakim refers to hakim, one who issues rules or decrees.
Allah, may He be exalted, is the One Who rules over His creation, and no one has the power to take away from Him His universal (kawni or qadari) rule and decree.
He is also the One Who issues decrees for His creation, so that they follow His religious (Shar‘i) decree, which no one can change or adjust.
Allah, may He be exalted, says (interpretation of the meaning):
{The decision [al-hukm] is only for Allah. He relates the truth, and He is the best of deciders.} [al-An‘am 6:57]
So no one could overturn His decree.
Allah, may He be exalted, says (interpretation of the meaning):
{And Allah decides; there is no adjuster of His decision. And He is swift in account.} [ar-Ra‘d 13:41]
And there is no decree better than His decree.
Allah, may He be exalted, says (interpretation of the meaning):
{And follow what is revealed to you, [O Muhammad], and be patient until Allah will judge. And He is the best of judges.} [Yunus 10:109]
Second meaning of Allah’s name Al-Hakim
Or it is the intensive form (“fa‘il”) of the “muf‘il” pattern, meaning that Allah is  muhkim or One Who is precise in His creation. 
Thus He, may He be glorified, created His creation in a precise manner and made it perfect and most beautiful. 
Allah, may He be exalted, says (interpretation of the meaning): 
{[It is] the work of Allah, who perfected all things. Indeed, He is Acquainted with that which you do.} [an-Naml 27:88]   
Al-Khattabi (may Allah have mercy on him) said:
“Al-Hakim is the One Who created with precision (muhkim) all things.
Precision in the creation of things refers to the fact that one may see the care of Allah in His creation and His proper estimation of them, for not all created beings have a strong and powerful build, such as gnats, ants and similar weak creatures, but what you see of divine care and brilliant design in their creation, and the fact that they point to the existence of the Creator, is to be added to what is indicative of the existence of the Creator in the creation of the heavens, the earth, the mountains and other mighty creations.
Similarly, in the verse in which Allah, may He be exalted, says (interpretation of the meaning): {Who perfected everything which He created} [as-Sajdah 32:7], this does not refer to that perfection or beauty that makes the onlooker pleased with what he sees, because that meaning of beauty does not exist in monkeys, pigs, bears and similar animals. Rather the meaning of perfection or beauty refers to precise divine care in creating everything that He created, in the manner in which He wanted it to be created, and bringing it into existence in the shape he wanted it to be in, as is mentioned in the verse (interpretation of the meaning): {… and has created each thing and determined it with [precise] determination} [al-Furqan 25:2]” (Shan ad-Du‘a, p. 73-74)
Third meaning of Allah’s name Al-Hakim
The third meaning of al-Hakim is the One Who is possessed of wisdom.
Ibn al-Athir said:
“It was said that al-Hakim means the One Who is possessed of wisdom, and wisdom refers to knowing the best of things by virtue of the best branches of knowledge.” (An-Nihayah fi Gharib al-Hadith, 1/419)
Allah, may He be glorified and exalted, does not run the affairs of this universe except on the basis of wisdom, and He does not enjoin or forbid anything except on the basis of wisdom. He does not do anything that is devoid of wisdom, because actions and deeds that are devoid of wisdom are actions that are in vain and without purpose, and Allah, may He be exalted, is far above that.
Allah, may He be exalted, says (interpretation of the meaning):
{And We did not create the heaven and the earth and that between them aimlessly. That is the assumption of those who disbelieve, so woe to those who disbelieve from the Fire.} [Sad 38:27]
{Then did you think that We created you without purpose and that to Us you would not be returned?".} [al-Muminun 23:115]
In conclusion, the divine name al-Hakim includes several interconnected meanings, between which there is no contradiction. So it may be interpreted on the basis of all of the meanings referred to above, because one divine name that has many meanings may be interpreted on the basis of all of its meanings, unless there is some reason not to do so. (See: Adwa al-Bayan by ash-Shinqiti, 2/19)
Shaykh as-Sa‘di (may Allah have mercy on him) said:
“Al-Hakim is the One to Whom belongs sublime wisdom in His creation and His command, Who has created everything in a perfect manner: {But who is better than Allah in judgement for a people who are certain [in faith]} [al-Maidah 5:50]. So He does not create anything in vain, or prescribe anything without purpose. The One Who has the power to decree and judge in this life and the Hereafter, to Him belong the three types of decrees and no one has any share with Him in them. Thus He decrees and judges between His slaves according to His shar‘i rulings, and according to His decrees and His requital. 
Wisdom means putting things in their right places.” (Tafsir as-Sa‘di, p. 945)
And Allah knows best.