Specifying -XX:ErrorFile=<path> only succeeds if there is not already a file at <path>. When there is, it will silently revert to the default path/filename which is hs_err... in the current directory:

java -XX:ErrorHandlerTest=13 -XX:ErrorFile=/tmp/hallo
#
# A fatal error has been detected by the Java Runtime Environment:
..
#
# An error report file with more information is saved as:
# /tmp/hallo

java -XX:ErrorHandlerTest=13 -XX:ErrorFile=/tmp/hallo
#
# A fatal error has been detected by the Java Runtime Environment:
#
...
#
# An error report file with more information is saved as:
# /shared/projects/openjdk/test/hs_err_pid14685.log
#

That is not useful.

More useful alternatives would be:
- append or overwrite the existing file
- create a new file with an appendix ("_<num>" or "_pid")