Matrix BUILD_TAG doesn't mention JOB_NAME.
Also, git tagging doesn't look like BUILD_NAME or BUILD_TAG (git tag looks like "hudson-test_matrix-3")

both of these are generated by env|sort and then had non-essential information removed. If you think there are some fields missing I can re-add them.

Simple build named 'test':

BUILD_ID=2009-03-27_16-32-56
BUILD_NUMBER=3
BUILD_TAG=hudson-test-3
EXECUTOR_NUMBER=0
HUDSON_HOME=/home/hudson
HUDSON_URL=http://hudson:8081/
JOB_NAME=test
WORKSPACE=/home/hudson/jobs/test/workspace

Matrix build named 'test_matrix', with parameter FOO=bar (or FOO=zyzzyx, not shown), and label=path_11

BUILD_ID=2009-03-27_15-09-32
BUILD_NUMBER=3
BUILD_TAG=hudson-FOO=bar,label=path_11-3
EXECUTOR_NUMBER=0
FOO=bar
HOME=/usr/hudson
HUDSON_URL=http://hudson:8081/
JOB_NAME=test_matrix/FOO=bar,label=path_11
LOGNAME=hudson
WORKSPACE=/usr/hudson/workspace/test_matrix/FOO/bar/label/path_11
label=path_11

note BUILD_TAG in test_matrix doesn't include teh string test_matrix, but BUILD_TAG in test DOES include the name fo the job.