When Yahoo switched to the new profile system they did not connect the information on that new profile with what shows on the chatters list in the chat room as your information.
To change this information you will have to access the old profile system. Even though the instructions for this are how to get a chat room nickname, it is the exact same place as you would change your location and age and have it show in the chat room.
CREATE A CHATROOM NICKNAME
If you mean how do you change your nickname that is used in the yahoo chat rooms, the new profile system is not connected to the chat room information in any way unlike the old profile system unless of course people view your profile. This also goes for the information, such as age and location, that you can read about a person by hovering over their name on the chat room's chatters list. The chat room nickname is also different from the nickname you can put in My Contact Details. Anyways to have a nickname for the chat room you need to access the old profile system. Who knows how long this method will work until Yahoo shuts it down too.
This link explains how to do it: http://www.helpbytes.co.uk/profilenickname.php . There are 2 methods to choose from. A shortcut method where you type your Yahoo ID in the box and click the button and the long URL that you copy and paste into the address bar of your browser. Remember to change the ending of the URL to your own Yahoo ID. For example in the URL it says <USERID> I would replace with true.colors (no brackets). On some names that short cut method doesn't work so you need to use the copy paste option. Please note you will be prompted to sign into your old profile with name and password.
Once you have made the changes on the old profile, click save changes on the lower right corner. Then exit Yahoo Messenger by right clicking the yahoo icon by your clock and choosing exit and then restart Yahoo Messenger. Now, your nickname should be visible when you enter the chat room.
