Unfortunately renaming or modifying existing connections is not supported. This is definitely a constraint that I would like to see reviewed in the future.
In our system we don't have write access to the database and thus had to take a different approach.
We created a new connection as you described but then exported and imported the project which allows you to map it to the new connection.
Be very careful with this though as there are a number of known issues with importing projects. If you are importing into a different project without deleting the rules from the original you have will duplicate rules names and the import will fail. Project is not part of the key because rules can be made public and referenced in multiple projects.
The project name can also be hardcoded into Views, Rules, and RuleBindings upon export. The import does not identify this and change the project name dynamically, causing failures.
There are separate threads on both these with more details. Would love to hear other approaches but that is all we have found.
