Need help with a query for a helpdesk application
Simply add another join to the tblUsers table, to get the name of the other employee.

SELECT p.pID
    , EmpFullName = uEmp.fName + ' ' + uEmp.lName
    , p.sLocation
    , p.sRoom
    , p.pStatus
    , p.pTitle
    , RepFullName = uRep.fName + ' ' + uRep.lName
FROM dbo.Problems p 
    INNER JOIN dbo.tblUsers uEmp ON p.employeeID = uEmp.empID
    INNER JOIN dbo.tblUsers uRep ON p.repID = uRep.empID
WHERE p.pStatus='OPEN';


As you can see, there are two instances of the dbo.tblUsers table referenced in the FROM clause, each with a different alias.  This allows you to return separate rows from tblUsers, one for the EmployeeID and one for the RepID

You'll likely need to add to the WHERE clause to pulls rows from the Problem table for a particular EmployeeID or a particular RepID depending on how you want to display results.  This might look something like:

WHERE p.pStatus='OPEN'
    AND p.empID = 42;


Notice, I've prefaced all tables in the FROM clause with the name of the schema where those tables reside.  This is a great habit to have since it will prevent issues down the road if you decide to have more than a single schema.

I also listed each column on its own row, and moved the column aliases in front of the actual column name in the SELECT clause; this makes it easier to find the particular column later when debugging.

You should also get in the habit of appending a semi-colon to the end of all T-SQL statements, since that can mitigate problems with the WITH CTE construct, among others.