Summary

As per https://docs.atlassian.com/jira-software/REST/server/#agile/1.0/board , it's currently not possible to rename boards via REST API

Suggestion

Add official REST endpoint to allow rename of boards via REST API

Workaround

Use the following (tested in JIRA 7.5.0)

• URL: /rest/greenhopper/1.0/rapidviewconfig/name
• Method: PUT
• Data:

  {
     "id":7,
     "name":"New Board Name"
  }

  Replace the board ID and new name accordingly. You can retrieve the board ID using GET /rest/agile/1.0/board