The three dot menu to the right of a connection name on the Connection manager allows to you both Edit connection and to Delete connection.
Edit connection links to the same configuration page used to create the connection, and you need to have the same security information (login, password, etc.) to change anything about the connection. Delete connection prompts you to be sure you want to proceed, but does not require any further validation.
Any organization admin or other authorized person with the credentials for a connection can modify it, and any data steward or other authorized person with access to the Connection manager can delete connections.