I am aware that as far as the ninety-nine (99) names of Allah are concerned, there are only around thirty five (35) or forty (40) that we know through the Holy Qur’ān and the Āhādīth. The rest we have derived. What I want to know is whether inferring the name of Allah in this way is okay. And also attributing names like Adārr (One who harms) just does not seem right because if any bad thing happens to us that is either a test or the result of our own wrong doings. What are the arguments for such a derivation? Secondly, what do you think about the Hadīth in which the Holy Prophet (sws) mentions that those who memorize ninety nine (99) names of Allah will go to Paradise? How can this Hadīth be the basis for going ahead and associating names with Allah? 

The Holy Qur’ān tells us that every good attribute that we may think of originally belongs to Allah. To quote some verses:

The fairest names are Allah’s. (7:180)

His are the most beautiful names. (17:110)

Allah! There is no God but Him. His are the most beautiful names. (20:8)

 Therefore, every good name that springs to our mind actually belongs to Allah because He is absolute good. The fact we must keep in mind is that while the Holy Qur’ān asserts that all beautiful names are Allah’s, nowhere does it claim that it has imparted to mankind an exhaustive list of His names. I therefore see nothing wrong with inferring good names of Allah from the Holy Qur’ān as well as from the Hadīth literature. Care however must be exercised that we do not ascribe to Him any name which in reality is not good.

I agree with you that we must avoid deriving such names as Adārr. We however can explain this name that although Allah does not cause harm to anyone in the minutest sense, He, it is, who allows bad things happen to someone, as per the divine law that He has established, sometimes through natural phenomena and sometimes through human beings themselves.

The Hadīth regarding memorizing the ninety-nine names of Allah has been reported in many great works of Āhādīth namely Sahīh Bukhāri, Sunan Tirmadhī, Sahīh Muslim and Musnad Ahmad. I quote here one from Sahīh Muslim:

Abū Hurayrah narrates: There are ninety-nine names of Allah, whoever commits them to memory would go to Paradise. Verily, Allah is odd [Allah is one and it is an odd number] and He loves odd numbers. (Muslim, No. 4835)

This Hadīth actually conveys to us that anyone who really believes in these ninety-nine attributes of Allah and always remembers them truly will be compelled to live a good life avoiding all the unseemly acts that may emanate from him in case He forgets the Lord. Thus, he, by remembering His Lord with all His attributes, will become entitled to enter Paradise because of the God-fearing life he leads in this world.

As for you question how this Hadīth could have been a source for deriving ninety-nine names of Allah, I would like to say since this Hadīth mentioned the figure ninety-nine, many people set about collecting and identifying the intended names. Thus, they ended up making a list that we have today with us. I personally feel that these Āhādīth only attempted to convey that there are innumerable good names of Allah. They did not intend to fix a number. The Holy Qur’ān also supports this viewpoint since it mentions that all good names are Allah’s.