I were wondering about this myself.
Since Ilia said the name is intended only for the admin in his vision, I can tell that this should be a hack - with source code modification. I haven't done this yet on my forum but that's a good occasion to do so:
You should modify the $DATA_DIR/src/usrinfo.php.t as following:
you have a set of similar short lines (121-130 for 2.6.0) like
$location = $u->location ? '{TEMPLATE: location}' : '';
add a line at the top of this block
$user_name = $u->name ? '{TEMPLATE: user_name}' : '';
Then you should modify $DATA_DIR/thm/default/trml/usrinfo.tmpl (or whatever theme you use in place of deafult) as following:
add the above mentioned TEMPLATE SECTION anywhere in upper part of the file between {SECTION: END} and next {SECTION: user_image} e.g. as following:
{SECTION: user_name}
<tr class="{ALT-VAR: search_alt RowStyleA RowStyleB}"><td nowrap class="GenText">{MSG: register_name}</td><td
class="GenText">{VAR: u->name}</td></tr>
{SECTION: END}
Then find the {PAGE_USERINFO line (186 for now)
scroll down to a start of a set of lines beginning with {TEMPLATE-DATA:
at the top of this block of similar lines add a line that will display the user_name actually
{TEMPLATE-DATA: user_name}
Now you're done, all the users can see each other names (if they entered it - it's not a required field in this forum normally).
I guess this thread should really be in hacks and let's hope moderators will move it there.