Given the republican, anti-British sentiment at the time of the American War of Independence, was there any thought given then to renaming the five southern colonies, all of which were named after English kings and queens?
Nope. No one seemed to have any problem with former kings and queens, just the, at the time, current one.
George Stewart, in Names on the Land, says the name changing among towns as a result of the Revolution was fairly minimal. Most of the examples of name changes he gives are of more locally known people rather than royalty. For instance, there was a William Tryon who was royal governor first of North Carolina and then New York. During the war he was appointed a general in the British army. Most of the places named for him were renamed to something else. Other examples were places named after locals who were loyalists during the war and thus unpopular.
I seem to remember that at least one place kept the name Georgetown but changed which George the place was named after.