diff --git a/django/db/backends/postgresql/base.py b/django/db/backends/postgresql/base.py
index 0c060e57eb..3537270897 100644
--- a/django/db/backends/postgresql/base.py
+++ b/django/db/backends/postgresql/base.py
@@ -9,7 +9,7 @@ import warnings
 
 from django.conf import settings
 from django.core.exceptions import ImproperlyConfigured
-from django.db import DEFAULT_DB_ALIAS
+from django.db import connections
 from django.db.backends.base.base import BaseDatabaseWrapper
 from django.db.utils import DatabaseError as WrappedDatabaseError
 from django.utils.functional import cached_property
@@ -255,16 +255,16 @@ class DatabaseWrapper(BaseDatabaseWrapper):
                 "to avoid running initialization queries against the production "
                 "database when it's not needed (for example, when running tests). "
                 "Django was unable to create a connection to the 'postgres' database "
-                "and will use the default database instead.",
+                "and will use the first PostgreSQL database instead.",
                 RuntimeWarning
             )
-            settings_dict = self.settings_dict.copy()
-            settings_dict['NAME'] = settings.DATABASES[DEFAULT_DB_ALIAS]['NAME']
-            nodb_connection = self.__class__(
-                self.settings_dict.copy(),
-                alias=self.alias,
-                allow_thread_sharing=False,
-            )
+            for connection in connections.all():
+                if connection.vendor == 'postgresql' and connection.settings_dict['NAME'] != 'postgres':
+                    return self.__class__(
+                        {**self.settings_dict, 'NAME': connection.settings_dict['NAME']},
+                        alias=self.alias,
+                        allow_thread_sharing=False,
+                    )
         return nodb_connection
 
     @cached_property
diff --git a/tests/backends/postgresql/tests.py b/tests/backends/postgresql/tests.py
index c4810c0960..43bd28eae9 100644
--- a/tests/backends/postgresql/tests.py
+++ b/tests/backends/postgresql/tests.py
@@ -2,7 +2,7 @@ import unittest
 import warnings
 from unittest import mock
 
-from django.db import DatabaseError, connection
+from django.db import DatabaseError, connection, connections
 from django.test import TestCase
 
 
@@ -26,10 +26,15 @@ class Tests(TestCase):
         with warnings.catch_warnings(record=True) as w:
             with mock.patch('django.db.backends.base.base.BaseDatabaseWrapper.connect',
                             side_effect=mocked_connect, autospec=True):
-                warnings.simplefilter('always', RuntimeWarning)
-                nodb_conn = connection._nodb_connection
+                with mock.patch.object(
+                    connection,
+                    'settings_dict',
+                    {**connection.settings_dict, 'NAME': 'postgres'},
+                ):
+                    warnings.simplefilter('always', RuntimeWarning)
+                    nodb_conn = connection._nodb_connection
         self.assertIsNotNone(nodb_conn.settings_dict['NAME'])
-        self.assertEqual(nodb_conn.settings_dict['NAME'], connection.settings_dict['NAME'])
+        self.assertEqual(nodb_conn.settings_dict['NAME'], connections['other'].settings_dict['NAME'])
         # Check a RuntimeWarning has been emitted
         self.assertEqual(len(w), 1)
         self.assertEqual(w[0].message.__class__, RuntimeWarning)