diff --git a/src/Storageless/Http/SessionMiddleware.php b/src/Storageless/Http/SessionMiddleware.php
index 7b8fb2f9..64e9972c 100644
--- a/src/Storageless/Http/SessionMiddleware.php
+++ b/src/Storageless/Http/SessionMiddleware.php
@@ -58,12 +58,14 @@ final class SessionMiddleware implements MiddlewareInterface
     private Configuration $config;
     private SetCookie $defaultCookie;
 
+    /** @param literal-string $sessionAttribute */
     public function __construct(
         Configuration $configuration,
         SetCookie $defaultCookie,
         private int $idleTimeout,
         private Clock $clock,
         private int $refreshTime = self::DEFAULT_REFRESH_TIME,
+        private string $sessionAttribute = self::SESSION_ATTRIBUTE,
     ) {
         $this->config        = $configuration;
         $this->defaultCookie = clone $defaultCookie;
@@ -130,7 +132,7 @@ public function process(Request $request, RequestHandlerInterface $handler): Res
 
         return $this->appendToken(
             $sessionContainer,
-            $handler->handle($request->withAttribute(self::SESSION_ATTRIBUTE, $sessionContainer)),
+            $handler->handle($request->withAttribute($this->sessionAttribute, $sessionContainer)),
             $token,
         );
     }
diff --git a/test/StoragelessTest/Http/SessionMiddlewareTest.php b/test/StoragelessTest/Http/SessionMiddlewareTest.php
index 2a3a4cc6..5dbb6abb 100644
--- a/test/StoragelessTest/Http/SessionMiddlewareTest.php
+++ b/test/StoragelessTest/Http/SessionMiddlewareTest.php
@@ -735,6 +735,34 @@ public function testMutableCookieWillNotBeUsed(): void
         );
     }
 
+    public function testAllowCustomRequestAttributeName(): void
+    {
+        $customAttributeName = 'my_custom_session_attribute_name';
+        self::assertNotEmpty($customAttributeName);
+
+        $middleware = new SessionMiddleware(
+            Configuration::forSymmetricSigner(
+                new Sha256(),
+                self::makeRandomSymmetricKey(),
+            ),
+            SetCookie::create(SessionMiddleware::DEFAULT_COOKIE),
+            100,
+            SystemClock::fromSystemTimezone(),
+            100,
+            $customAttributeName,
+        );
+
+        $middleware->process(
+            new ServerRequest(),
+            $this->fakeDelegate(static function (ServerRequestInterface $request) use ($customAttributeName) {
+                self::assertInstanceOf(SessionInterface::class, $request->getAttribute($customAttributeName));
+                self::assertNull($request->getAttribute(SessionMiddleware::SESSION_ATTRIBUTE));
+
+                return new Response();
+            }),
+        );
+    }
+
     private function ensureSameResponse(
         SessionMiddleware $middleware,
         ServerRequestInterface $request,