If you just renamed Webmin user (using Webmin Users module), it means there would be no correspondent UNIX user, that could be used with default authentication method, which is set to Unix authentication by default (for default root user) and which you most likely didn’t change to Webmin password authentication by selecting Set to… from the drop down menu:
Either way the simplest solution to your problem would be using a new webmin passwd command to change the password and set Webmin password authentication automatically:
Example:
webmin passwd --user username