I tried to save dashboard and report via Salesforce Reports and Dashboards REST API and it works, but when I change developerName in the request body and send this request, in the response I got a json body with saved metadata of Report/Dashboard and parameter developerName hasn't been changed.
I also used update and upsert methods of the Salesforce SOAP API, but in the response I got the next message:

<message>entity type cannot be updated: Report</message>
<statusCode>CANNOT_INSERT_UPDATE_ACTIVATE_ENTITY</statusCode>