This simple command works like a charm:
git name-rev <SHA>
For example (where test-branch is the branch name):
git name-rev 651ad3a
251ad3a remotes/origin/test-branch
Even this is working for complex scenarios, like:
origin/branchA/
/branchB
/commit<SHA1>
/commit<SHA2>
Here git name-rev commit<SHA2>
returns branchB.