Currently the branch build results are combined with regular plan results, and it's confusing. For example, getting a branch name via a REST API call can be done by this call:
http://localhost:8085/rest/api/latest/result/PROJ1-PLAN11
and the shortName will contain the branch name:
... <plan enabled="true" type="chain_branch" shortKey="PLAN11" shortName="master" name="Project-1 - Plan-1 - master" key="PROJ1-PLAN11"> ...
Having a separate REST API service for plan branches will make working with them more straightforward.