The name that's used for the live trading room's chat features is whatever you enter when you log into the room. Below is a screenshot of how the login form appears for the room. Whatever you enter under the Name field is what is used as your chat room name.
Since there may be several people who share the same first name, some people like to use an identifier that may include their location, such as Bob N. from VT. But you can use what you're comfortable with. You would probably benefit from being consistent from day to day as people do get to know one another in the room by their name.
To change your name, exit the room, and reenter with a new name specified in the room login form that appears when you enter the live trading room. Note that you do NOT need a password to enter the live trading room, as you're already authenticated as a platinum member when you log into the BCT website. You do want to provide the email you use to log into the BCT website in the email field.
For more details about this and other helpful info about the live trading room, refer to this knowledge base article.