there is no relation whatsoever between COBOL PROGRAM ID and member name per se...
when the compiler is invoked the compiler itself will not be aware from where the source program comes from
( it is just reading a PD dataset )
member name being the same as the PROGRAM ID depends only on strictly/loosely enforced standards.
is it required and used by some change management packages ??? strict standard
Your organization tells You so, a bit more loose one ( if not checked somehow )
When I tell somebody to RTFM or STFW I usually have the page open in another tab/window of my browser,
so that I am sure that the information requested can be reached with a very small effort