From its origins as a conduit to pay hush money, Essential Consultants LLC has evolved into a nexus in federal investigations buffeting the Trump administration.

Michael Cohen, President Donald Trump’s personal attorney, set up the Delaware limited liability company to pay former adult-movie actressStephanie Clifford, professionally known as Stormy Daniels. Now the company has become a central piece of an investigation, led by the Manhattan U.S. attorney’s office, into whether Mr. Cohen committed federal bank fraud, money...