Is there a verb that describes someone from the countryside (ie: new in town ) who tries to behave , dress and speak like its people to fit in and not be taken for a redneck ?
The most apposite verb is acculturate, meaning "to assimilate a different culture".
Here is an example:
There are a few ways to say this. The nice way would be to say he is trying to fit in.
Something that adds a little zing but isn't too bad is saying that he is conforming.
If the person is reluctant or was out of their realm then you can say they gave in or they were acquiescent.