As I said, this is a property of the system.
The system can be configured to do anything, don't core dump, core dump but overwrite any previous core dump, core dump in some special directory taking care not to overwrite anything, etc[1]. Of course, a process can ask for special treatment, but Go binaries are no different than default C binaries.
[1] http://man7.org/linux/man-pages/man5/core.5.html