Should I output program's name when warning or error occurs?

It is common practice to save the 0th argument passed to a C program main and use that as the parameter for perror — for simple programs:

#include <stdio.h>
#include <stdlib.h>

int main(int argc, char *argv[])
{
    char *foo = malloc(9999999999L);
    if (foo == 0)
        perror(argv[0]);
    return 0;
}

call that program "foo", and running it illustrates the point:

> ./foo
./foo: Cannot allocate memory

Complicated programs may add to the text (or use only the filename without the path), but keeping the program name lets you find where a misbehaving program came from.

There is no universally accepted scheme for error messages, but some widely-used programs (such as gcc) add a message category such as "Error" or "Warning". Here's an example from one of my build-logs:

compiling fld_def (obj_s)
../form/fld_def.c: In function '_nc_Copy_Argument':
../form/fld_def.c:164:14: warning: cast discards 'const' qualifier from pointer target type [-Wcast-qual]
        res = (TypeArgument *)argp;
              ^

In this example, gcc separates fields with colons and adds a category "warning" after the filename, line number, column number — and before the actual message. But there are several variations, making it complicated for programs (such as vi-like-emacs) to parse the information.

For compilers, using a category in the message makes it simple to detect the fatal errors (which may not be immediately fatal) and warnings. If your program exits on an error it does not add much to say that some are really warnings and some are errors. But when it behaves differently (or continues to work more or less) the category helps to diagnose the problem encountered.

If a program is invoked as part of a script in which many other programs are invoked, and if it doesn't print its name, then users will find it hard(er) to figure out where the error is coming from.

(If the error is some unexpected internal condition that may require debugging, you want even more info: not just the program name, but a source file and line number and possibly a backtrace.)