Is it discouraged to have names that are ending with ‘uddin’, or is it just an opinion of some scholars?
This is what the article of Islamqa says;
It is makruh to use any name which is composed of any word added to such words as al-Din (the Religion) or Islam, such as Nur al-Din/Nuruddin (Light of the Religion), Diya al-Din/Ziauddin (Brightness of the Religion), Sayf al-Islam (Sword of Islam), Nur al-Islam (Light of Islam), etc.
This is because of the great status attached to these words, al-Din and Islam. Adding words to them to form names is an exaggeration which borders on lying, which is why some scholars said that this is haram, and the majority say that it is makruh, because it gives an incorrect impression which should not be given. The way this practice started was that these were titles which were added to people’s names, then people started to use them as names.
Names of this sort may be forbidden for two reasons. In a name such as Shihab al-Din, for example, the word Shihab means a flame, which comes from fire, then this is added to the word al-Din (which is inappropriate). This can lead to the use of strange names, as in Indonesia, where people use names such as Dhahab al-Din (gold of the Religion) and Mas al-Din (diamond of the Religion)!
Imam al-Nawawi (may Allah have mercy on him), used to dislike being called by his nickname Muhiy al-Din, and Shaykh al-Islam Ibn Taymiyah (may Allah have mercy on him) used to dislike being called by his nickname Taqiy al-Din, and he said, But my family gave me this nickname, so I am known by it.