How Many Names Does Allah Have?
Question

Are there only ninety-nine names of Allah, or are there more than that?
Praise be to Allah.Al-Bukhari (2736) and Muslim (2677) narrated from Abu Hurayrah (may Allah be pleased with him) that the Messenger of Allah (peace and blessings of Allah be upon him) said: “Allah has ninety-nine names, one hundred less one. Whoever learns them will enter Paradise.” 
Some of the scholars (such as Ibn Hazm – may Allah have mercy on him) understood this hadith as meaning that the names of Allah are limited to this number. (Al-Muhalla, 1/51)
But what Ibn Hazm said is not supported by the majority of scholars. Rather some of them (such as al-Nawawi) narrated that the scholars agreed that the names of Allah are not limited to this number. It seems that they regarded the view of Ibn Hazm as odd and as something that should not be paid any attention.
In support of the view that the beautiful names of Allah are not limited to this number, they quoted the report narrated by Ahmad (3704) from ‘Abd-Allah ibn Mas’ud who said: The Messenger of Allah (peace and blessings of Allah be upon him) said: “There is no-one who is afflicted by distress and grief, and says: ‘Allahumma inni ‘abduka ibn ‘abdika ibn amatika nasyati bi yadika, madin fiyya hukmuka, ‘adlun fiyya qada-uka. As-aluka bi kulli ismin huwa laka sammayta bihi nafsaka aw anzaltahu fi kitabika aw ‘allamtahu ahadan min khalqika aw istatharta bihi fi ‘ilm il-ghayb ‘indaka an taj’al al-Qurana rabi’a qalbi wa nura sadri wa jala-a huzni wa dhahab hammi (O Allah, I am Your slave, son of Your slave, son of Your maidservant; my forelock is in Your hand, Your command over me is forever executed and Your decree over me is just. I ask You by every name belonging to You which You have named Yourself with, or revealed in Your Book, or You taught to any of Your creation, or You have preserved in the knowledge of the Unseen with You, that You make the Quran the life of my heart and the light of my breast, and a departure for my sorrow and a release for my anxiety),’ but Allah will take away his distress and grief, and replace it with joy.” He was asked: “O Messenger of Allah, should we learn this?” He said: “Of course; everyone who hears it should learn it.” (Classed as sahih by al-Albani in al-Silsilah al-Sahihah, 199) 
The phrase “or You have preserved in the knowledge of the Unseen with You” indicates that there are beautiful names of Allah that He has kept with Him in the knowledge of the Unseen, and which none of His creation has come to know. This indicates that there are more than ninety-nine Names. 
Shaykh al-Islam [Ibn Taymiyah] said concerning this hadith in Majmu’ al-Fatawa (6/374):  
“This indicates that Allah has more than ninety-nine names.” 
And he said (22/482): 
Al-Khattabi said: 
“This indicates that He has names that He has preserved with Him, and that indicates that the words “Allah has ninety-nine names , whoever learns them will enter Paradise” mean that there are ninety-nine of His names which whoever learns them will enter Paradise. This is like saying, “I have one thousand dirhams which I have prepared to give to charity,” even if his wealth is greater than that. In the Quran Allah says (interpretation of the meaning): 
“And (all) the Most Beautiful Names belong to Allah, so call on Him by them.” [al-A’raf 7:180]
Allah has commanded us to call upon Him by His names in general terms, He did not say that He has only ninety-nine names. 
Al-Nawawi (may Allah have mercy on him) stated in Sharh Sahih Muslim that the scholars were unanimously agreed on that, and he said: 
“The scholars unanimously agreed that this hadith does not mean that Allah has only ninety-nine names, or that He does not have any other names apart from these ninety-nine. Rather what the hadith means is that whoever learns these ninety-nine will enter Paradise. The point is that one may enter Paradise by learning them, not that the number is limited to these names.” 
And Shaykh Ibn ‘Uthaymin was asked about that and replied: 
“The names of Allah are not limited to a certain number. The evidence for that is the words of the Prophet (peace and blessings of Allah be upon him) in the sahih hadith: “O Allah, I am Your slave, son of Your slave… I ask You by every name belonging to You which You have named Yourself with, or revealed in Your Book, or You taught to any of Your creation, or You have preserved in the knowledge of the Unseen with You.” 
What Allah has preserved in the knowledge of the unseen with Him cannot be known and what is not known is unlimited. 
With regard to the words of the Prophet (peace and blessings of Allah be upon him), “Allah has ninety-nine names, one hundred less one. Whoever learns them will enter Paradise,” this does not mean that He does not have any names apart from these, rather it means that whoever learns these ninety-nine of His names will enter Paradise. This is like when the Arabs say: “I have one hundred horses which I have prepared for jihad for the sake of Allah,” which does not mean that the speaker has only these hundred horses, rather these hundred are prepared for this purpose.” (Majmu’ Fatawa Ibn ‘Uthaymin, 1/122)
For more, please see this category: Names and Attributes of Allah
And Allah knows best.