INSERT statement COPY equivalent
The point of COPY is to receive the data from outside the query.
The closest syntax to what you're asking is

COPY users(username) FROM STDIN;


If done from within the psql interpreter in interactive mode, it displays this invite:


  Enter data to be copied followed by a newline. End with a backslash
  and a period on a line by itself, or an EOF signal.


If done from a non-interactive program, dedicated functions can be used to send the data. They're provided by the PostgreSQL driver that the program uses.