You write:
I am looking for a Git command that will print the symbolic name for HEAD.
The following may suffice to demonstrate that what you're asking for does not make sense in all situations, simply because HEAD may not be unambiguously associated with one reference. Read on.
What git name-rev does
In the git-name-rev man-page, you find the following description:
Given a commit, find out where it is relative to the local refs. [...]
More specifically, git name-rev checks whether <commit-ish> is reachable from any of the local references (by processing them in lexicographical order, e.g. develop before master).
Let's examine what
$ git name-rev --name-only <commit-ish>
does in different cases (the --name-only flag is incidental here, as its effects are purely cosmetic).
Case in which HEAD is not detached
If HEAD is not detached, i.o.w. if HEAD is pointing to a valid ref (let's call it myref), then there is no ambiguity: running
$ git name-rev --name-only HEAD
simply outputs
myref
because the myref reference is unambiguously associated with HEAD. So far, so good.
Case in which HEAD is detached
In that case, things are not as simple. In fact, there may be one or more references from which <commit-ish> is reachable, or there may be none at all.
Case in which there are one or more such local references
At the first such local reference found, git name-rev prints a "relative" symbolic reference, i.e. a revision of the form
<ref>~<n>
where <ref> stands for the local reference in question, and <n> stands for the generation. For example, if HEAD points directly to a commit that is a grandparent of master (master being the only local reference), then
$ git name-rev HEAD
returns
master~2
Note, however, that in case <commit-ish> is reachable from multiple references, the one returned by git name-rev is somewhat arbitrary, as it's only dictated by the lexicographical order (in which the command checks local references).
Case in which there is no such local reference
It's easy to imagine situations in which <commit-ish> is reachable from none of the local references. Actually, here is one you can reproduce at home (boilerplate stdout is omitted):
# set things up
$ mkdir test
$ cd test
$ git init
# create a commit
$ touch README.md
$ git add README.md
$ git commit -m "add README"
# detach the HEAD (make it point directly to the tip of master, instead of to master itself)
$ git checkout $(git rev-parse master)
# create a second commit (while in detached-HEAD state)
$ printf "foo\n" > README.md
$ git commit -am "write 'foo' in README"
# attempt to find a symbolic name for HEAD 
$ git name-rev --name-only HEAD
undefined
Because the commit DAG looks as follows,
A [master]
 \
  B [HEAD]
commit B is not reachable from the only reference (master); therefore, git name-rev gives up and simply returns undefined.
Conclusion
Because HEAD is not guaranteed to be unambiguously associated to one reference, what you're asking for doesn't make sense :p