Hey @IWhite,
Unfortunately, this is currently not a feature of the HubSpot Service Hub. I can understand, though that coming from a different software, you would want as much similar functionality as possible.
Without knowing too much about your company, organization and processes, it might also be an opportunity to review current processes and habits.
It’s a good practice to think of ownership of specific records like tickets, and HubSpot leans heavily on that idea. A person gets assigned manually or via automation to a ticket and therefore is the one responsible for handling the issue or request.
You can take a look here to get more insights on how to do owner assignment.
If you haven’t already, maybe this is something exploring more in your case
Cheers,
Chriso