Does it make sense to say God is the son of himself?
In case of the names, be they different or describing the same glory, at the end, "The Creator" is "The Merciful" is "The Graceful" etc.. so it's different.
Why is God a trinity then in Christianity, why don't they include the person "Graceful", the person "Merciful", the person "holy", etc, because "persons" it's not attributes. When Christianity doesn't consider attributes showing different persons, then obviously it's not the same as the trinity which is different persons. So it makes no sense to compare it with attributes.
For example stating God is King doesn't show a different person, then stating God is the Creator. They are denoting the same being.
Is father a description of the son? Is an attribute of the son? No... so you are comparing something completely different.
As to avenging denoting the same glory as the Mercy is, yeah, according to scholars of Islam, it is, every name of God is said to be complete beauty...so they all encompass each other.
The following is from Khomeini:
The Qur'an says: Call Allah or call Rahman (Surah al-Isra', 17:110). In another verse it says: Call Him by any name, for all the beautiful names are His. (Surah al-A'raf, 7:180) Allah, Rahman, Rahim and all other names of Him are good and beautiful. Each of them combines all His attributes. He being Absolute, there is no disparity between Him and His names or between one of His names and another. Allah's beautiful names are not like the names we give to different things for different considerations. His glory and His manifestation are not two different aspects of Him. His manifestation is exactly His glory and His glory exactly His manifestation. Even this expression is defective. Absolute existence means Absolute perfection and Absolute perfection must be absolute in every respect. Therefore, all His attributes are absolute. No disparity of any sort can be imagined between His essence and His attributes.