From the DOT Publication Best Practices for Random Drug and Alcohol Testing.

Notify each employee discreetly, following your company’s policy. Conduct random testing in strict confidence, involving only a limited number of people who know the selection list. Why? This approach maintains the element of surprise.
Best Practices: Set clear procedures to ensure each employee receives no advance notice of selection. Allow enough time for supervisors to arrange the test and confirm collection site availability.

Remember: Employers must ensure proper privacy for the individual during the testing process.