Thank you for your query!
This can definitely be automated by using our API, you can then pull a unique identifier (like the Serial number) and the Computer name. These variables can then be used to create the bomgar.ourwebsite.com/ComputerName variable and push this to a custom field in SolarWinds Service Desk.
We have a similar example for updating the Hardware owner for computers, here. You can use this example as a starting point or contact your SolarWinds Service Desk Account Manager if you are in need of further assistance with this.
Hope this helped!
SolarWinds Service Desk