doc: Fix description of how the default user name is chosen

This makes the distinction between operating-system user name and
database user name a bit clearer.  It also clarifies that the user
name is determined first, and then the default database name.

Author: David G. Johnston <david.g.johnston@gmail.com>
Discussion: https://www.postgresql.org/message-id/flat/CAKFQuwZUhgz=sUi+wGQV-PBTNjMovuA-BOV88RV-Vw0m0drCAg@mail.gmail.com

doc/src/sgml/client-auth.sgml

@@ -2313,7 +2313,7 @@ FATAL:  database "testdb" does not exist
 </programlisting>
     The database you are trying to connect to does not exist. Note that
     if you do not specify a database name, it defaults to the database
-    user name, which might or might not be the right thing.
+    user name.
    </para>
 
    <tip>

doc/src/sgml/ref/psql-ref.sgml

@@ -646,23 +646,24 @@ EOF
     <application>psql</application> is a regular
     <productname>PostgreSQL</productname> client application. In order
     to connect to a database you need to know the name of your target
-    database, the host name and port number of the server, and what user
-    name you want to connect as. <application>psql</application> can be
-    told about those parameters via command line options, namely
+    database, the host name and port number of the server, and what
+    database user name you want to connect as. <application>psql</application>
+    can be told about those parameters via command line options, namely
     <option>-d</option>, <option>-h</option>, <option>-p</option>, and
     <option>-U</option> respectively. If an argument is found that does
     not belong to any option it will be interpreted as the database name
-    (or the user name, if the database name is already given). Not all
+    (or the database user name, if the database name is already given). Not all
     of these options are required; there are useful defaults. If you omit the host
     name, <application>psql</application> will connect via a Unix-domain socket
     to a server on the local host, or via TCP/IP to <literal>localhost</literal> on
     Windows. The default port number is
     determined at compile time.
     Since the database server uses the same default, you will not have
-    to specify the port in most cases. The default user name is your
-    operating-system user name, as is the default database name.
+    to specify the port in most cases. The default database user name is your
+    operating-system user name. Once the database user name is determined, it
+    is used as the default database name.
     Note that you cannot
-    just connect to any database under any user name. Your database
+    just connect to any database under any database user name. Your database
     administrator should have informed you about your access rights.
     </para>