I wanted to ask you all about reading Surah Yaseen 72 times in state of distress or for a specific cause and also if making Dhikr of Allah's Names in a specific number for a specific cause is permissible.

Praise be to Allah, the Lord of the Worlds; and may His blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions.

No doubt that reading Qur'an has great merits and is highly rewarded. The reciter of Qur'an is given the reward of 10 good deeds for every letter of the Qur'an he recites. There are sound Hadith proving this.
As for the Surah "Yasin" [36] and the reward of reciting it and memorizing it, there are some Ahadith about this. But these Ahadith do not reach the level of correctness. Here are some of these Ahadith. al-Tabarani reported in 'al-Saghir' that the Prophet (Sallallahu Alaihi wa Sallam) said: "Whoever reads Yasin permanently dies a martyr" .
Abu Dawood reported from M'aqal Ibn Yasar that the Prophet (Sallallahu Alaihi wa Sallam) said: "Read Yasin on your dead people" . al-Shawkani said: ' al-Bazar reported from Ibn Abbas that the Prophet (Sallallahu Alaihi wa Sallam) said: "I wish strongly that (Yasin) be in the heart of everyone of my Ummah" .
Although these Ahadith do not reach the level of soundness but they together prove the great merits of Surah Yasin.
As for reading it a number of times or reading it in order to solve some problems, we have not come across any evidence for it.
For the honoured Attributes of Allah, it is likable to use them in Du'a and call Allah with them. Allah Says (interpretation of meaning): {And (all) the Most Beautiful Names belong to Allâh, so call on Him by them, …} [7: 180].
There is no limit to the remembrance of Allah. So anyone who wants to have his Du'a answered should multiply remembering Allah and calling Him with His Attributes.
Allah knows best.