Your Yahoo! ID is the key to your master account. Once you've registered with Yahoo! and chosen a Yahoo! ID, you cannot change it.
However, you can play games under an alias without revealing your primary Yahoo! ID. To create or edit an alias, the first step is to view your Yahoo! Profile. Click "Create New Public Profile" and fill out the form. Then click "Create Profile" at the bottom of the page when you're done.
Once you've created an alias, return to a game ante room (where you select a lounge to play in). You can select the ID you'd like to play under from the drop-down list near the top of the game's ante room (where the list of lounges is).
Please note: If you wish to play using an ID from a different Yahoo! account (not just an alias), click the "edit - sign out" link at the top of the page. Then you can return to Yahoo! Games and sign in with your other ID.