No option to "Edit" a Messaging channel

To edit a messaging channel, the Org and the User must meet the below three requirements:

1. Omni-Channel must be enabled and configured for Messaging
2. The "Messaging User" permission set license must be assigned to the user
3. The user must be assigned to a permission set with the 'Configure Messaging' permission

To enable Omni-Channel:

1. Navigate to Setup > Omni-Channel Settings
2. Check the "Enable Omni-Channel" checkbox

To assign the "Messaging User" Permission Set License:

1. Navigate to the User's record via Setup > Users
2. Click the Username
3. Scroll down to Permission Set License Assignments related list and click the "Edit Assignments" button
4. Check the "Enabled" box for the "Messaging User" Permission Set License

To create a Permission Set for Messaging:

1. Navigate to Permission Sets via Setup > Permission Sets
2. Click the "New" button
3. Under App Permissions, enable the permission "Configure Messaging". Save.
4. Click the button "Manage Assignments" to add the desired users to the Permission Set and click "Save".

Note: If you don't see the App Permission "Configure Messaging" in the newly created Permission Set, check if you assigned this Permission Set to a specific License. To prevent licenses incompatibilities, leave the default value 'None' in the field "License", when creating this Permission Set.     


Once these actions have been completed, the user should see the option to "Edit" messaging channels.

More details on Messaging Permission Sets can be found in this article.