For me, Richard Eaton’s The Rise of Islam and the Bengal Frontier, 1204–1760, is the best analysis of the peculiar spatial distribution of religion in South Asia today. This is not because Eaton’s work is without flaw, or beyond reproach. It is because few have made as concerted an effort to analyze this issue in a dispassionate manner.
The map to the right shows the proportion of Muslims within united Bengal in ~1870 by region. The outlines of Bangladesh and West Bengal are already clear. That being said, one feature that seems clear is that the more marginal areas are curiously mostly Muslim (e.g., the far southeast). Eaton’s broad argument, following upon others, is a consequence of the fact that these areas came under intensive cultivation only during the Mughal period, and therefore under the aegis of Muslim elites. Therefore, the local peasantry took up a nominal Muslim identity as a matter of course. To reinforce the mechanism, Eaton points out that there are noted cases of villages founded by Hindu zamindars in the east where Hindu shrines were built, and the peasants nominally adhered to the sect of Hinduism professed by the zamindar.
The Rise of Islam and the Bengal Frontier, 1204–1760 is fully available online. I encourage you to read it. One thing that is now clearer to me again after reading it is that Islam as a religious identity of the peasantry of eastern Bengal is a notable feature only after the Mughal conquest of 1576. Visitors to Bengal from other regions before this date mention Muslims only as residents of cities and towns. Additionally, these Muslims often have some foreign connection, whether it be Afghan, Turk, or Persian. As far as the rural people go, none are mentioned as Muslim. Some of them described in eastern Bengal also seem likely to have been Tibeto-Burman in origin. They are described as “beardless”, and Muslim commentators assert they are neither the religion of India nor are they Muslims.
After 1600 visitors began to observe large numbers of Muslims in places such as the lands on either side of the Meghna river. In contrast, observers of the Hooghly basin note that all the inhabitants are Hindus (e.g., a Jesuit declares they are all “idolaters”).
In another paper Eaton analyzes Punjab. While the Islamicization of Bengal was driven by small mosques and shrines in newly founded hamlets, Eaton argues that in western Punjab Islamcization was driven by the transition of pastoralist Jatts to farming, and their settlement around charismatic Sufi shrines. But, he presents data that suggests that this process of Islamization was gradual and somewhat later than the present-day Muslims assert. Siyal Jatts of Jhang in northern Punjab assert they have been Muslim since 1250. But a record of names of notables from this community suggests this is unlikely.
Islamicization began in the period between 1400 and 1500. But the shift from Punjabi names to self-conscious Muslim names did not complete in totality until 400 years had passed.