diff --git a/doc/src/sgml/config.sgml b/doc/src/sgml/config.sgml
index d42b7d63ee..e639f1d26d 100644
--- a/doc/src/sgml/config.sgml
+++ b/doc/src/sgml/config.sgml
@@ -6886,9 +6886,9 @@ local0.*    /var/log/postgresql
         The name will be displayed in the <structname>pg_stat_activity</structname> view
         and included in CSV log entries.  It can also be included in regular
         log entries via the <xref linkend="guc-log-line-prefix"/> parameter.
-        Only printable ASCII characters may be used in the
-        <varname>application_name</varname> value. Other characters will be
-        replaced with question marks (<literal>?</literal>).
+        Characters that are not printable ASCII, like <literal>\x03</literal>,
+        are replaced with the <productname>PostgreSQL</productname>
+        <link linkend="sql-syntax-strings-escape">C-style escaped hexadecimal byte value</link>.
        </para>
       </listitem>
      </varlistentry>
@@ -7883,11 +7883,13 @@ COPY postgres_log FROM '/full/path/to/logfile.csv' WITH csv;
        <para>
         The name can be any string of less
         than <symbol>NAMEDATALEN</symbol> characters (64 characters in a standard
-        build). Only printable ASCII characters may be used in the
-        <varname>cluster_name</varname> value. Other characters will be
-        replaced with question marks (<literal>?</literal>).  No name is shown
-        if this parameter is set to the empty string <literal>''</literal> (which is
-        the default). This parameter can only be set at server start.
+        build).
+        Characters that are not printable ASCII, like <literal>\x03</literal>,
+        are replaced with the <productname>PostgreSQL</productname>
+        <link linkend="sql-syntax-strings-escape">C-style escaped hexadecimal byte value</link>.
+        No name is shown if this parameter is set to the empty string
+        <literal>''</literal> (which is the default). This parameter can only
+        be set at server start.
        </para>
       </listitem>
      </varlistentry>
diff --git a/doc/src/sgml/postgres-fdw.sgml b/doc/src/sgml/postgres-fdw.sgml
index 5062d712e7..f6b60ffdba 100644
--- a/doc/src/sgml/postgres-fdw.sgml
+++ b/doc/src/sgml/postgres-fdw.sgml
@@ -1064,12 +1064,12 @@ postgres=# SELECT postgres_fdw_disconnect_all();
      </para>
      <para>
       <varname>postgres_fdw.application_name</varname> can be any string
-      of any length and contain even non-ASCII characters.  However when
-      it's passed to and used as <varname>application_name</varname>
+      of any length and contain even characters that are not printable ASCII.
+      However when it's passed to and used as <varname>application_name</varname>
       in a foreign server, note that it will be truncated to less than
       <symbol>NAMEDATALEN</symbol> characters and anything other than
-      printable ASCII characters will be replaced with question
-      marks (<literal>?</literal>).
+      printable ASCII characters are replaced with the <productname>PostgreSQL</productname>
+      <link linkend="sql-syntax-strings-escape">C-style escaped hexadecimal byte value</link>.
       See <xref linkend="guc-application-name"/> for details.
      </para>