Assign a quick action button to each employee.
To do this, open any order and go to the Quick Actions list.
Click Create quick action.
Enter the necessary parameters, including the responsible employee and save
Now go on to employees list.
Then open the parameters of your employee (who you have created the quick action for).
Set necessary Can run own quick actions checkboxes.
From the list of quick actions, select the created action.
Do all the actions above for each employee.
And then when employee creates or confirms customer's order with his quick action he will be automatically assigned to this order.
After that, create a table. In the table settings, filter orders by employee name.
This way, you will see all the orders assigned to the specific employee.
You will also see the name of the responsible employee in the order cart.
You can also configure a personal table for your employee.
More on this here