test -z $username expands to test -z a b which is a syntax error, because test -z only expects one argument. By adding double quotes, like test -z "$username", the expansion becomes test -z "a b" which has only a single, double-quoted argument. That will fix the syntax error.

However, test -z only checks for an empty string, but will treat a string with characters in it (even if they are blanks) as non-empty. I would recommend that you try the case approach instead. If it doesn't work, perhaps you can follow up here.

Not to sound too harsh, but I already explained this in how to check if a string consist of any space?