You can set up an automation rule under Admin > Workflows > Automations > Ticket updates > New Rule to send out satisfaction surveys to customers when the ticket is assigned to a specific group. 

When an action performed by.. 


Involves any of these events

Status is changed > Any status > Resolved

On ticket with these properties

In tickets > If Group > Is any of > Support


Send email to requester > (you can add the content of the notification email and insert the placeholder for Satisfaction Survey)