Mohun Bagan is name of a place in Kolkata, where the club was founded.
East Bengal was named much before formation of Bangladesh, in fact even before, Indian Independence when modern day Pak, Bangladesh all were under the same umbrella. as @goalkeepar mentioned it represented the people coming from East part of Bengal. and thus the rivalry started, now of course things are different, so easy to misinterpret the meaning of the names
East bengal formed in 1920s when the region was part of india after partation east bengal (region) became east pakistan and after 1971 war it became bangladesh.
why should they change the name? they still represent the people who came from East Bengal. Just because East Bengal is now a part of different country doesn't mean the culture, the sentiments regarding that is gone.
Plus East Bengal and Mohun Bagan have established fan bases and a real history and rivalry. Really, the only problems with the clubs are their structures.
Comments
http://eastbengalfootballclub.com/legacy.php?p=the-rise-of-east-bengal-club
And don't know what exactly Mohun Bagan means. Maybe @rudra knows.