Note that there are characters in nicknames that cannot be used in filenames or INI sections, and are replaced by an underscore instead. This has the potential to create nickname collisions.
What doesn't make sense to me is the fact that each file is unique to their nickname, so there's no reason to use their nickname again in the ini section. Just use the literal word "nick" instead.
Otherwise, here's a simple method to rename an INI section that seems to work just fine.
/writeini -n test.ini foo bar baz
/write -s[foo] test.ini [fum]