Question

Why Mughals didn't like to be called Mughals?

Answer 1

It is So because Mughals might didn't like to be associated with those who destroyed whole Khwarazmian dynasty and killed their fellow Muslims.

Answer 2

$\mathfrak{The\:Answer\:is}$

India was ruled for over 200 years by the Gurkani, a clan that established an empire of such magnificence, size and wealth, that it became a byword for glory around the world. But the name by which the Gurkani became rightly famous was an aberration. The dynasty was a nomadic Timurid one, as the founder, Babur, proudly traced his lineage directly to the Turkic conqueror, Amir Timur ( also known as Tamerlane), who established an empire in the 14th century quite as glorious as Chinghiz Khan’s.

Babur refered to himself, and to his lineage, as Gurkani, from the Persianized Mongol word for Guregen, or son-in-law, since some of the Timurids, including Amir Timur, has marriages Chingizid women, to add their legitimacy.

But Babur himself, and all of his descendants, male and female, were intensely proud of their Timurid lineage, very consciously evoking the Timurid charisma in various ways.

Indeed, Babur thoroughly loathed his Mongol cousins, the Uzbeks, considering them brutish and uncivilised.

Babur would have been horrified to know that his dynasty would become synonymous with an Anglicised form of Mongols-the Mughals of India.

$\boxed{Hope\:This\:Helps}$