Conditional Join - Specific Column Select
Regarding your comment about the scan, that happens because using ISNULL() in the join manipulates the field, so it's no longer SARGable. It may be faster to split this up, rather than try to do all the work in a single query. For example:

DECLARE @Recipient_ID INT, @Submitter_ID INT

SELECT 
@Recipient_ID = Order.Recipient_Id, 
@Submitter_ID = Order.Submitter_Id
FROM Order
-- where clauses

IF @Recipient_ID IS NULL

SELECT Emp.Full_Name
FROM Employee Emp
WHERE Emp.Emp_Id = @Submitter_ID

ELSE

SELECT Emp.Full_Name
FROM Employee Emp
WHERE Emp.Emp_Id = @Recipient_ID


EDIT based on comment:
Since there can be many orders, what about this? It is SARGable so should index well, and you're not querying the table multiple times.

with cte as (
SELECT 
COALESCE(Order.Recipient_Id, Order.Submitter_Id) AS EmployeeID
FROM Order
-- where clauses
)

SELECT Emp.Full_Name
    FROM Employee Emp
INNER JOIN cte on cte.EmployeID = Emp.Emp_Id