Although this is an old question, I had the same question when using the Standard console version. The answer can be found in the Debian Live manual under the section 10.1 Customizing the live user. It says:
It is also possible to change the default username “user” and the
default password “live”.
I tried the username user and password live and it did work. If you want to run commands as root you can preface each command with sudo