diff --git a/twisted/web/server.py b/twisted/web/server.py
index a48f2ea..1a66d32 100644
--- a/twisted/web/server.py
+++ b/twisted/web/server.py
@@ -101,9 +101,12 @@ class Request(Copyable, http.Request, components.Componentized):
     @ivar defaultContentType: A C{bytes} giving the default I{Content-Type}
         value to send in responses if no other value is set.  C{None} disables
         the default.
+    @ivar sessionCookieBaseName: A C{bytes} giving the base name when creating
+        new session cookies.
     """
 
     defaultContentType = b"text/html"
+    sessionCookieBaseName = b'TWISTED_SESSION'
 
     site = None
     appRootURL = None
@@ -384,7 +387,8 @@ class Request(Copyable, http.Request, components.Componentized):
     def getSession(self, sessionInterface = None):
         # Session management
         if not self.session:
-            cookiename = b"_".join([b'TWISTED_SESSION'] + self.sitepath)
+            cookiename = b"_".join(
+                [self.sessionCookieBaseName] + self.sitepath)
             sessionCookie = self.getCookie(cookiename)
             if sessionCookie:
                 try:
diff --git a/twisted/web/test/test_web.py b/twisted/web/test/test_web.py
index 46b66f2..5ce9eeb 100644
--- a/twisted/web/test/test_web.py
+++ b/twisted/web/test/test_web.py
@@ -466,6 +466,22 @@ class RequestTests(unittest.TestCase):
         request.requestReceived(b'GET', b'/foo%2Fbar', b'HTTP/1.0')
         self.assertEqual(request.prePathURL(), b'http://example.com/foo%2Fbar')
 
+    def test_getSessionCustomCookieName(self):
+        """
+        When creating new session cookies it will use
+        I{Request.sessionCookieBaseName} as the base name for the new cookie.
+        """
+        baseName = b'CUSTON_NAME'
+        channel = DummyChannel()
+        request = server.Request(channel, 1)
+        request.sitepath = []
+        request.site = channel.site
+        request.sessionCookieBaseName = baseName
+
+        session = request.getSession()
+        self.addCleanup(lambda: session.expire())
+
+        self.assertTrue(request.cookies[0].startswith(baseName))
 
 
 class GzipEncoderTests(unittest.TestCase):
diff --git a/twisted/web/topfiles/6933.feature b/twisted/web/topfiles/6933.feature
new file mode 100644
index 0000000..b097862
--- /dev/null
+++ b/twisted/web/topfiles/6933.feature
@@ -0,0 +1 @@
+twisted.web.server.Request allows specifying a custom name for session cookie.
\ No newline at end of file