My issue is more about the size of Dorchester than it's current bad name. Dorchester was once a city like Cambridge or Brookline that was annexed to Boston. So as Cambridge has vastly different sections, so too does the former city of Dorchester.
I live in a Victorian neighborhood of triple deckers. Lower Mills is brick-and-beam loft buildings. Ashmost is large, grandiose mansions on rolling lawns. Four Corners is apartment tenements.... every neighborhood is so unique and so different that it is tough to generalize and just call it all "Dorchester".
In my part of Dorchester, I'm actually closer to Beacon Hill than I am to other parts of Dorchester! It's that big.
I'm quite proud to say I live in Dorchester, but it's hard when such a wide swath of Boston goes by one loose, general name. A model that I like is how there is West Roxbury and Roxbury. For a land mass a huge as Dorchester, why not a "South, East, West, North" Dorchester?
We're getting a little off topic of Lower Mills - but in my mind, Lower Mills is a world away from my neighborhood in both distance and character... even though to the rest of the world it's all just "Dorchester"