Update how to get support (docker#5801)

* Update how to get support

* Address feedback

Author: joaofnfernandes

datacenter/dtr/2.4/guides/support.md

@@ -5,12 +5,15 @@ description: Your Docker subscription gives you access to prioritized support. Y
 keywords: support, help
 ---
 
-Your Docker Data Center, or Docker Trusted Registry subscription gives you
-access to prioritized support. The service levels depend on your subscription.
+Your Docker Enterprise Edition subscription gives you access to prioritized
+support. The service levels depend on your subscription.
 
-If you need help, you can file a ticket via:
+Before reaching out to Docker Support, make sure you're listed as an authorized
+support contact for your account. If you're not listed as an authorized
+support contact, find a person who is, and ask them to open a case with
+Docker Support in your behalf.
 
-* [Email](mailto:support@docker.com)
-* [Docker support page](https://support.docker.com/)
-
-Be sure to use your company email when filing tickets.
+You can open a new support case at the [Docker support page](https://support.docker.com/).
+If you're unable to submit a new case using the support page, fill in the
+[Docker account support form](https://success.docker.com/support) using your
+company email address.

datacenter/ucp/2.2/guides/get-support.md

@@ -7,12 +7,15 @@ keywords: support, help
 Your Docker Enterprise Edition subscription gives you access to prioritized
 support. The service levels depend on your subscription.
 
-If you need help, you can file a ticket via:
-
-* [Email](mailto:[email protected])
-* [Docker support page](https://support.docker.com/)
-
-Be sure to use your company email when filing tickets.
+Before reaching out to Docker Support, make sure you're listed as an authorized
+support contact for your account. If you're not listed as an authorized
+support contact, find a person who is, and ask them to open a case with
+Docker Support in your behalf.
+
+You can open a new support case at the [Docker support page](https://support.docker.com/).
+If you're unable to submit a new case using the support page, fill in the
+[Docker account support form](https://success.docker.com/support) using your
+company email address.
 
 Docker Support engineers may ask you to provide a UCP support dump, which is an
 archive that contains UCP system logs and diagnostic information. To obtain a