Ben Bernanke was appointed to the board and chairman at the same time in 2006. Or I should say reappointed since he'd been on the Fed board from 2002 to 2005 and resigned to become head of Bush's Council of Economic Advisers. Alan Greenspan was appointed directly to the Fed chairmanship by Reagan. Paul Volker was appointed Fed Chair from his position as President of the New York Fed. Trump could have appointed anyone he wanted to, on the board or off.
“As stipulated in the Banking Act of 1935, the Chair and Vice Chair of the Board are two of seven members of the Board of Governors who are appointed by the President from among the sitting Governors.”
“The Chairman and the Vice Chairman of the Board are named by the President from among the members and are confirmed by the Senate. “
https://www.federalreserve.gov/aboutthefed/bios/board/default.htm