BuzzFeed News found President Joe Biden’s Venmo account after less than 10 minutes of looking for it, revealing a network of his private social connections, a national security issue for the United States, and a major privacy concern for everyone who uses the popular peer-to-peer payments app.

On Friday, following a passing mention in the New York Times that the president had sent his grandchildren money on Venmo, BuzzFeed News searched for the president’s account using only a combination of the app’s built-in search tool and public friends feature. In...