All perfect praise be to Allah the Lord of the Worlds. May Allah`s peace and blessings be upon our Prophet Mohammad and upon all his family and companions.
As regards the beautiful names of Allah, some are specific to Him the Almighty and none may be called by them except Him, such as Allah, Ar-Rahman (The Beneficent) and Al-Khaaliq (The Creator, The Maker), in addition to other names that only befit His Majesty, so it is impermissible call humans with them.
However, some names may be given to Allah and humans, such as Al-Kareem (The Most Generous, The Most Esteemed) and Al-`Alim (The All-Knowing) and other. When Allah calls Himself with these names, they befit Him, His Majesty, His Perfection and His Greatness. However, when these names are given to a human, they indicate his imperfection and weakness. Names of Tazkiah aren`t entirely Makruh (Reprehensible). Rather, what is Makruh is intending to be praised by virtue of the name itself. As if the person holding the name is saying that he enjoys the qualities of piety and righteousness embodied in the name itself. It was narrated from Abu Hurairah that: "Zainab used to be called "Barrah" (good), and it was said that she was praising herself. So the Messenger of Allah (Peace be upon him) changed her name to Zainab." {Related by Muslim}.
If the holder of the name isn`t arrogant and doesn`t brag with it, then it is permissible to be given that name. Rather, the beautiful names of Allah that carry the meanings of piety and righteousness are recommended, and it is hoped that the meanings of the names are reflected in their holders.
In addition, it is Makruh to give a child an ugly name and it is recommended to change such name. This is based on the following narration: Ibn ‘Umar said : "The Messenger of Allah (May peace be upon him) changed the name of ‘Asiyah and called her Jamilah." {Muslim}.
The name "Mu`min" is neither specific to Allah the Almighty nor a cause of pessimism. This is because the feature of faith in this name is a constant one and inconceivable to be removed from it, so there is no sin in keeping this name. And Allah the Almighty knows best.