If you use the usermod command recommended above, you would need to chown anything because the the uid hasn't changed.
If you do it by hand by editing the passwd file, you can find the files you need to chmod and chmod them with the following command.
sudo find / -uid XXX | while read filename ;do chmod USER "$filename" ; done
Replace XXX with the old uid # and USER with the new username. There are fancy shell ways of avoiding the while;read, but this works very well and works in virtually any shell. You can score points if you tell me what I am doing it this way.