How do I get the name of the parent branch?

Google results point to how to get to commits that have gone into
parent branches, but fundamentally I just want to have a script
that constructs a diff of what has changed since the latest branch
without having to do manual research to figure out the name.

As best as I can tell, you use:

    git format-patch -o pdir --ignore-if-in-upstream $branch

the hard part seems to be (but ought not be) figuring out
the value for "$branch".