It wasnt built and named in terms of conquest; it was to be a unity of the two cultures. Unlike the Christians (Catholics I will use loosely) the Muslims allowed other religions to be practiced within their territories without consequence. The Ottoman and Safavid Empires were for tolerant of other peoples’ religion and culture unlike that of the Catholics. So much so that even the Ottoman Empire helped out the Protestant side during the Thirty Years War aka the Holy Wars in the 1500s. The Muslim faith has been very welcoming of others unlike that of Catholic who would go, kill and destroy that went anything remotely against their faith, be it Muslim, Jew, then Protestant, then Scientific Revolution.
So don’t talk about Muslim conquest, when the Christians have been doing it since the death of Jesus well before the start of the Islamic faith in 617.