proxy_set_header not working as expected

As per CGI specification, http headers are availabe with the HTTP_ prefix:

Meta-variables with names beginning with "HTTP_" contain values readfrom the client request header fields, if the protocol used is HTTP.The HTTP header field name is converted to upper case, has alloccurrences of "-" replaced with "_" and has "HTTP_" prepended togive the meta-variable name.

That is, header Some-Header will be seen as HTTP_SOME_HEADER in your application. That is, everything works is expected - you added http header, and got it available with HTTP_ prefix.

The SCRIPT_NAME variable is special and isn't set by any header, but instead it's constructed from URI by the code which runs your application. To change it, you have to actually change URI seen by your backend, i.e. you need

proxy_pass http://localhost:4567/wiki/;

Or just no /wiki/ in proxy_pass, as long as it's in location /wiki/ anyway, i.e.

location /wiki/ {    proxy http://localhost:4567;}

The bad thing here is that you probably did URI change from /wiki/ to / for some reason, i.e. your backend application expects /. There are several possible solutions to this problem:

1. Actually move the application to /wiki/. Usually this is simple to do.
2. Change your app to accept it's base url used for generating links etc. by some out-of-bands method. Many application already support this via some configuration option.
3. Try to replace what your application returns by nginx itself. There are several nginx directives to do it, in particular proxy_redirect, proxy_cookie_path, and the sub filter. It's most fragile method though, and not recommended unless you know what your application returns and what exactly have to be replaced.