Change labels on ‘Nickname’ and ‘Biographical Info’ in user-edit.php

Every string goes through translate(), which uses the gettext filter. This mean you can try something like this:

add_filter( 'gettext', 'wpse6096_gettext', 10, 2 );
function wpse6096_gettext( $translation, $original )
{
    if ( 'Nickname' == $original ) {
        return 'Funny name';
    }
    if ( 'Biographical Info' == $original ) {
        return 'Resume';
    }
    return $translation;
}

It’s probably even more efficient if you only call the add_filter when you are on the user-edit.php page (see the admin_head-user-edit.php hook or something like that).