Question

why mugshots don't liked to be called from their mother side(genghis khan)?​

Answer 1

Although they were known as Mughals because of their Mongolian descent, they did not like being referred to as Mughals because the name of the Mongols has been marred by massacres and bloodshed.
Because the word Mughal was connected with Mongols and Genghis Khan who killed many people, the Mughals did not like being called that.