A more porcelain way:
git log -n 1 --pretty=%d HEAD
# or equivalently:
git show -s --pretty=%d HEAD
The refs will be listed in the format (HEAD, master) – you’ll have to parse it a little bit if you intend to use this in scripts rather than for human consumption.
You could also implement it yourself a little more cleanly:
git for-each-ref --format="%(objectname) %(refname:short)" refs/heads | awk "/^$(git rev-parse HEAD)/ {print \$2}"
with the benefit of getting the candidate refs on separate lines, with no extra characters.