I have often wondered this, Same thing with town names and street names.
Firstly the 'why didnt they...' questions so often used here often imply that 'an event was gonna happen, but then something stopped it, what was that something?'. However this isnt always the case. That is, there is no specific clear and concise reason this did not occur, its more that in most places no one really wanted it to occur.
In this specific situaion I think the answer as to why there wasnt a demand to change names is based on a modern misconception.
Although modern ... um... populist historical rhetoric suggests that freedom loving Americans rose up aganst the evil tyranny of British overlordship, the actual beliefs and opinions about the colonists towards Britain seem a lot less black an white. They may have been against 'the system', but they werent, as far as I've read, so much against the people.
That is, the British colonists revolted against an unjust system and replaced it with their own, but that doesnt mean they hated the Brits or even entirely thought that they werent 'British' in some way. It takes time to forge an identity, many of the colonists were born in Britain or were only first generation. Many would have had strong ethnic ties to Britain, they didnt feel the need to deny or dispute this. Thus this independence movement is of a different form than where one ethnic grouping gains freedom from the overlordship of another.
A further issue is that where they may have been proposals to change, you might have found that a certain inertia occurs when faced with a multitude of alternative names vying to replace a name you've grown used to. New York IS New York, its based on the old York from Yorkshire, but it is not the 'lesser' of the two cities. Its proud of what it is. How many people would want it changed to Franklintown (after Benjamin) or something. Does anyone today (who are way less British and far more 'ethnically' American than anyone of 1776) want to expunge the names? Almost entirely not.
Some may have been altered at the time, virtualmayhem seems to think so, but these appear to be an exception as far as I can see. Perhaps, conjecture here, these places already had a new identity that hadnt cemented yet, or they were named after someone people REALLY didnt like.
This is an interesting questuon, especially considering that some town names were changed, I believe. I imagine that because the colonies (and their names) had been established between 100 and 170 years before the Revolution, the origin of those names may not have occurred to them.