Well, not exactly.
Many presidents, like George Washington, had no middle name. And some who did didn't use it.
Ronald Wilson Reagan took the oath simply as Ronald Reagan. Richard Milhous Nixon used his middle name at his first inauguration, but dropped it at his second.
James Earl Carter was "Jimmy." But it was William Jefferson Clinton, not Bill. Gerald Rudolph Ford used his middle initial. And Stephen Grover Cleveland, Thomas Woodrow Wilson and John Calvin Coolidge dropped their first names.
Some didn't use their names at all, simply saying "I" solemnly swear, or just answering "I do" after the chief justice read the oath. And the record for the most names? George Herbert Walker Bush.