In the long view of history, everybody is an invader. Throughout history all over the world people have invaded and conquered new territory, settled down there and then been invaded in turn. The theorized Aryan migration in India (which possibly lead to the demise of the Indus valley civilization), the Greeks who settled after Alexander, the push backs, the Cholas invading cities in Indonesia etc.
What is important is that: these invasions occurred at a time when conquest by force and invasion was perfectly natural and that many of the soldiers of the invading forces settled down and became indigenized.
From the Pakistani point of view, their history is inherently linked to the history of Islam in India, since their very origin was as a home for the Muslims of the sub-continent. Islam was frequently spread by the sword and the invaders are essentially the founding fathers of the Islamic identity in India (Ghauri -> Qutb-ud-din Aibak -> Delhi Sultanate, India’s first Islamic dynasty. Babur -> Mughals.)
Similarly, all the other invaders too were noted for spreading or conserving Islam (Timur called himself the Sword of Islam). Hence, from their cultural point of view, it is as sensible for them to name themselves from their cultural ancestors as it is for Mongolia to identify with Genghis Khan, for Thailand (a Buddhist nation) to have kings named with a decidedly Hindu style etc.