In the Name of Allah, Most Gracious, Most Merciful.
All praise and thanks are due to Allah, and peace and blessings be upon His Messenger.
Dear questioner! Thank you for your question and the confidence you place in our service and we pray to Allah to enable us render this service purely for His Sake.
There is nothing wrong in using the 99 Names of Allah in supplication. A Muslim can use each name that suits what he is asking for. For example, one may say, “O Merciful! Shower mercy on me!” However, there is nothing authentic that indicates that a person has to use certain names for certain purposes after Prayer or on a certain day.
In acts of worship, we should take only what is proven by the authentic texts of the Shari`ah. Imam Al-Qurtubi wrote:
A person uses every name with its meaning, like he uses the name “The Merciful” while praying for mercy and “The Guide” while praying for guidance and “The Provider” while praying for provision. As for using general names, he can use such names for any meaning. Still, there is nothing in the authentic references that says that the 99 names are to be recited on a certain occasion or after a certain Prayer on a certain day. Also, there is nothing reported to say that some of the 99 names have some effects on healing diseases or the like. A Muslim should use the names only for general supplication that suits their meanings and the like.
Answering your question, Sheikh Muhammad Saleh Al-Munnajid, a prominent Saudi Muslim scholar and lecturer, states:
There is no sound basis for reciting these adhkar (plural of dhikr—remembering Allah) or the names of Allah in certain numbers. These numbers are usually stated by some of the innovators, most of whom are Sufis, who describe adhkar and the number of times they are to be repeated, making that up themselves; they say whoever recites such-and-such will get such-and-such benefits and protection, and whoever recites such-and-such a wird (daily quota of supplication) will get such-and-such a reward.
Of course, these are matters which can only be known through revelation. So the basic principle in this case is that dhikr and supplication are of two types:
1- Adhkarthat were narrated in the Qur’an and the Sunnah, to be recited at a certain time, in a certain place, or in certain circumstances. This type should be recited as prescribed, at the appropriate time, or in the appropriate circumstances or place, with the correct words or posture, without adding anything or taking anything away.
2- All adhkar or supplications in general that are not connected to certain times or places. These fall into two categories:
3- Those that were narrated from the Prophet (peace and blessings be upon him), so they should be recited in the wording that he used. They should not be connected to any particular time or place, and they should not be connected to a specific number of times to be recited.
4- Those that were not narrated from the Prophet (peace and blessings of Allah be upon him), rather the person makes them up himself, or they were narrated from the Salaf (the righteous early Muslims). It is permissible to say such words so long as five conditions are met:
(1) One should choose the best and clearest words, for one is conversing with one’s Lord and God.
(2) The words should be of an appropriate style.
(3) The supplication should be free of anything that is forbidden in Islam, e.g., it should not involve any element of seeking help from anyone or anything other than Allah, and so on.
(4) It should be of the general kind of dhikr and supplication, not connected to a particular time, place, or circumstance.
(5) It should not be taken as a regular practice.” (Adopted from Tashih Ad-Du`a’ by Sheikh Bakr Abu Zayd )
Based on the above, the names of Allah are narrated in the Qur’an and the Sunnah, but saying that they must be repeated a certain number of times is an innovation (bid`ah) that should not be followed. Rather we should mention the names of Allah in our supplications and address Allah by all His beautiful names, without singling out some names or stating that they should be recited a certain number of times or at certain times, making that up ourselves. We should adhere to what was narrated in Shari`ah concerning certain times, places, or situations connected to a particular supplication. If no such details were narrated in Shari`ah, then we should not make them up ourselves because that is encroaching upon the rights of Prophethood.
Almighty Allah knows best.
Excerpted with minor modifications from: www.islamqa.info