diff --git a/src/Platforms/SqlitePlatform.php b/src/Platforms/SqlitePlatform.php
index b4709721eb1..db51b682624 100644
--- a/src/Platforms/SqlitePlatform.php
+++ b/src/Platforms/SqlitePlatform.php
@@ -1016,7 +1016,7 @@ public function getAlterTableSQL(TableDiff $diff)
     private function replaceColumn($tableName, array $columns, $columnName, Column $column): array
     {
         $keys  = array_keys($columns);
-        $index = array_search($columnName, $keys, true);
+        $index = array_search(strtolower($columnName), $keys, true);
 
         if ($index === false) {
             throw SchemaException::columnDoesNotExist($columnName, $tableName);
diff --git a/src/Schema/SqliteSchemaManager.php b/src/Schema/SqliteSchemaManager.php
index 94529e2557f..1895fc4e1dd 100644
--- a/src/Schema/SqliteSchemaManager.php
+++ b/src/Schema/SqliteSchemaManager.php
@@ -577,4 +577,13 @@ public function createComparator(): Comparator
     {
         return new SQLite\Comparator($this->getDatabasePlatform());
     }
+
+    /**
+     * {@inheritDoc}
+     */
+    public function getSchemaSearchPaths()
+    {
+        // SQLite does not support schemas or databases
+        return [];
+    }
 }
diff --git a/tests/Functional/Platform/RenameColumnTest.php b/tests/Functional/Platform/RenameColumnTest.php
index fea9a2e25fd..4cc9ccb667f 100644
--- a/tests/Functional/Platform/RenameColumnTest.php
+++ b/tests/Functional/Platform/RenameColumnTest.php
@@ -10,16 +10,23 @@
 
 class RenameColumnTest extends FunctionalTestCase
 {
-    public function testColumnPositionRetainedAfterRenaming(): void
+    /**
+     * @dataProvider columnNameProvider
+     */
+    public function testColumnPositionRetainedAfterRenaming(string $columnName): void
     {
+        if ($columnName === 'C1') {
+            self::markTestIncomplete('See https://github.com/doctrine/dbal/issues/4816');
+        }
+
         $table = new Table('test_rename');
-        $table->addColumn('c1', 'string');
+        $table->addColumn($columnName, 'string');
         $table->addColumn('c2', 'integer');
 
         $sm = $this->connection->createSchemaManager();
         $sm->dropAndCreateTable($table);
 
-        $table->dropColumn('c1')
+        $table->dropColumn($columnName)
             ->addColumn('c1_x', 'string');
 
         $comparator = new Comparator();
@@ -31,4 +38,13 @@ public function testColumnPositionRetainedAfterRenaming(): void
         $table = $sm->listTableDetails('test_rename');
         self::assertSame(['c1_x', 'c2'], array_keys($table->getColumns()));
     }
+
+    /**
+     * @return iterable<array{string}>
+     */
+    public static function columnNameProvider(): iterable
+    {
+        yield ['c1'];
+        yield ['C1'];
+    }
 }
diff --git a/tests/Functional/Schema/SchemaTest.php b/tests/Functional/Schema/SchemaTest.php
new file mode 100644
index 00000000000..c4241268f45
--- /dev/null
+++ b/tests/Functional/Schema/SchemaTest.php
@@ -0,0 +1,17 @@
+<?php
+
+declare(strict_types=1);
+
+namespace Doctrine\DBAL\Tests\Functional\Schema;
+
+use Doctrine\DBAL\Schema\Schema;
+use Doctrine\DBAL\Tests\FunctionalTestCase;
+
+class SchemaTest extends FunctionalTestCase
+{
+    public function testSchemaName(): void
+    {
+        $schema = new Schema([], [], $this->connection->createSchemaManager()->createSchemaConfig());
+        self::assertNotEmpty($schema->getName());
+    }
+}