In the book 'Surprise, Kill, Vanish: The Secret History of CIA Paramilitary Armies, Operators, and Assassins' by Annie Jacobsen, she mentions this effect when the US Army stood up the secretive 10th Special Forces after WWII. Even though it was the first of its kind the idea was that if the U.S.S.R found out about it they would worry there were 9 other such groups.

This differs by branch of service in the United States.

The UK actually has its regiments ordered by seniority