Our faith in Allah includes everything that Allah's names and attributes entail. We believe everything that Allah tells us about Himself in the Qur'ân and everything that the Prophet Muhammad (peace be upon him) informed us about regarding Allah.
We believe that Allah is al-Rahmân (the Beneficent), al-Rahîm (the Merciful), al-Khâliq (the Creator), al-Razzâq (the Provider), as we believe in all of His sublime attributes.
It is enjoined upon us to call upon Allah by His names when we beseech Him in prayer. Each one of His names is rich in meaning, each telling us something more about Allah. Each is suitable for any of our various supplications.
However, there is a habit that some people have of assigning certain of Allah's names to beseeching specific needs or to asking Allah to cure particular illnesses. This practice is unfounded. The Prophet (peace be upon him) did not prescribe the use of specific names for specific needs.
We as Muslims should refrain from becoming formulistic in our supplications without any scriptural basis for doing so, but we should rather supplicate sincerely from our hearts, calling upon Allah with the names that come to mind for what we are asking for.
There are certain supplications that we find in the Prophet's example that he offered on particular occasions. These supplications naturally include mention of Allah's names.
For example, the Prophet taught us to say in times of distress [Sahîh al-Bukhârî
(5870) and Sahîh Muslim
There is no God but Allah, the Mighty, the Gentle. There is no God but Allah, Lord of the Magnificent Throne. There is no God but Allah, Lord of the Heavens and Lord of the Earth and Lord of the Noble Throne.
Then there is the supplication for healing. A’ishah relates that the Prophet (peace be upon him) would seek protection for members of his family by wiping them with his right hand over them and reciting the following supplication [Sahîh al-Bukhârî
O Allah! Lord of humanity! Cure as you are the Curer. There is no cure except for your cure… a cure that will not leave any illness behind.
We should recite these supplications when the occasion arises for them. Otherwise, we should not single out certain names of Allah and recite them on specific occasions or when supplicating for particular needs. What we can do is simply call upon Allah with the name that we feel to be best suited for our needs when we supplicate Him.
We can beseech Allah as al-Razzâq (the Provider), saying for instance: "O Allah, you are the Provider. Provide for me." Likewise, we can say: "O `Azîz (Almighty), strengthen me." What is important is that we do not treat these practices as if they were ritual formula or as if they were specifically prescribed for us.
And Allah knows best.