The Exalter, The Elevator, The Raiser.
Allah is Ar-Rafi (in Arabic: ٱلْرَّافِعُ). He is The One who lowers whoever He wills and raises whoever He wills. The One who chooses who will be raised in rank in every way.
From the root ra-fa-ayn (ر ف ع), which has the following classical Arabic connotations: to raise or elevate something, to uplift, to take it up, to make high, to exalt, make honorable, make eminent, to bring a thing near.
This name is contrasted with Al-Khafid, meaning The Reducer. Just as Allah سُبْحَٰنَهُۥ وَتَعَٰلَىٰ can lower, He has the power and ability to raise. He honors certain individuals like the Prophets (may peace be upon them), who are still revered to this day. Others have been disgraced, like Abu Lahab, the uncle of Prophet Muhammad ﷺ who has an entire Surah debasing Him (i.e., Surah al-Masad).
Among the disputed names:
Different scholars have different criteria for what qualifies as a name of Allah سُبْحَٰنَهُۥ وَتَعَٰلَىٰ. Of the 99 names, 81 are explicitly mentioned in the Qur'an. Therefore, there is not one agreed-upon list for the remaining 18 names. Ar-Rafi is one of those names which has been excluded by some scholars. This includes Ibn Uthaymeen, Ibn Hazm, and Ibn Hajar, among others. However, Ar-Rafi is commonly recognized as an official name in most books of Asmaul Husna.
Wa tilka hujjatunaaa aatainaahaaa Ibraaheema ‘alaa qawmih; narfa’u darajaatim man nashaaa’; inna Rabbaka Hakeemun ‘Aleem
"And that was Our [conclusive] argument which We gave Abraham against his people. We raise by degrees whom We will. Indeed, your Lord is Wise and Knowing." — (Qur'an 6:83)
Yaaa ayyuhal lazeena aamanoo izaa qeela lakum tafassahoo fil majaalisi fafsahoo yafsahil laahu lakum wa izaa qeelan shuzoo fanshuzoo yarfa’il laahul lazeena aamanoo minkum wallazeena ootul ‘ilma darajaat; wallaahu bimaa ta’maloona khabeer
"O you who have believed, when you are told, “Space yourselves” in assemblies, then make space; Allah will make space for you. And when you are told, “Arise,” then arise; Allah will raise those who have believed among you and those who were given knowledge, by degrees. And Allah is Acquainted with what you do." — (Qur'an 58:11)
Rafee’ud darajaati zul ‘Arshi yulqir rooha min amrihee ‘alaa mai yashaaa’u min ‘ibaadihee liyunzira yawmat talaaq
"[He is] the Exalted above [all] degrees, Owner of the Throne; He places the inspiration of His command upon whom He wills of His servants to warn of the Day of Meeting." — (Qur'an 40:15)
An example from the story of Iblees:
The story of Iblees encapsulates these two names perfectly. It is yet another example of how if Allah سُبْحَٰنَهُۥ وَتَعَٰلَىٰ chooses, He can either exalt or debase. The popular belief among scholars is that Iblees was not an Angel but among the Jinns. But he was a high-ranking and pious one devoted to Allah سُبْحَٰنَهُۥ وَتَعَٰلَىٰ.
The reasoning for him being among the Jinn is that "..angels stern (and) severe, who flinch not (from executing) the Commands they receive from Allah, but do (precisely) what they are commanded." (Qur'an 66:6). Angels have no free will and carry out the commandments of Allah سُبْحَٰنَهُۥ وَتَعَٰلَىٰ, there is no disobedience. We're also told by Aishah (May Allah be pleased with her) that The Messenger of Allah ﷺ said, "Angels were created from light, jinns were created from a smokeless flame of fire, and 'Adam was created from that which you have been told (i.e., sounding clay like the clay of pottery)." 
The confusion as to whether Iblees was an Angel comes from this verse, "And [mention] when We said to the angels, 'Prostrate before Adam'; so they prostrated, except for Iblees. He refused and was arrogant and became of the disbelievers." (Qur'an 2:34) The exclusion 'except Iblees' seems to imply He was among the Angels. Al-Qurtubi said in his tafsir of Surah Baqarah: "The idea that he was one of the angels is the view of the majority [i.e., of the early sahaba], Ibn Abbas, Ibn Mas'ud, Ibn Jurayj, Ibn al-Musayyib, Qutadah and others." But in Surah Kahf, it is made clear, "And [mention] when We said to the angels, 'Prostrate to Adam,' and they prostrated, except for Iblees. He was of the jinn and departed from the command of his Lord." (Qur'an 18:50) Still the view among some is he was an Angel and then became of the Jinn upon his refusal. He was given the privilege to be the only one among the Angels when Allah سُبْحَٰنَهُۥ وَتَعَٰلَىٰ revealed to them His latest creation in Adam (as). But in Surah Sad, when Allah سُبْحَٰنَهُۥ وَتَعَٰلَىٰ asked why he refused to prostrate to Adam, "He said, 'I am better than him. You created me from fire and created him from clay.'" (Qur'an 38:76).
From these verses and the hadith, it seems clear the popular opinion should be that Iblees was a high-ranking Jinn who became debased. "[Allah] said, 'Get out of here; surely you are rajim accursed, And indeed, upon you is My curse until the Day of Recompense.'" (Qur'an 38:77-78)
Allah سُبْحَٰنَهُۥ وَتَعَٰلَىٰ raised the rank of Muhammad ﷺ:
In Surah Ash-Sharh verse 4, Allah سُبْحَٰنَهُۥ وَتَعَٰلَىٰ reminds Prophet Muhammad ﷺ He had raised his status to comfort him. Remember that this was an early Meccan surah when the Prophet was relatively unknown, with a few followers.
Wa raf ana laka zikrak
"And raised high for you your repute." — (Qur'an 95:4)
The believer benefits from the knowledge of this name. It re-affirms the reality that Ar-Rafi is the one we should rely upon. Allah سُبْحَٰنَهُۥ وَتَعَٰلَىٰ is high above all, so whatever it is you wish to be increased in, call upon this name. Only Allah سُبْحَٰنَهُۥ وَتَعَٰلَىٰ can increase your ranks; there is no other.
Be detached from your wrong-doings. Your wrong-doings are not you. Similarly, avoid the goal seeking to be raised because it creates a trap for yourself. What happens if you don't feel your status being elevated? Do you lose hope and motivation and stop seeking it from Allah? Imam Zarruq writes, "Whosoever comes to understand that He is Al-Khafid Ar-Rafi does not place his trust in any of his states, and he settles with no reliance on any component of his knowledge or any action of his. Besides, he desires neither a lowering nor an uplifting, since the two of them are not gained saved through Him." The one who worships Allah because they understand only He is worthy of worship, regardless of their emotional state or in success or poverty.
Imam al-Ghazali writes regarding his counsel for this name, "Man's share in this consists in exalting the truth and abasing falsehood, by supporting those who are right and reporaching those who are wrong, treating God's enemies as enemies in order to abase them and befriending God's friends in order to exalt them."
 Sahih Muslim 2996 & Riyad as-Salihin 1846