Yes, but the BJS code has been created since the name change, and NAY is also a relatively recent opening.
You would have thought they'd be keener to use the new code. The new terminal was still British designed & European bank financed, but I don't expect my local 'Chinese' takeway to serve up Beijing Duck anytime soon (
afaik they are mainly from HKG anyway).
Not sure what code proposed Navi Mumbai International Airport will take, and whether that will result in a new code for BOM.