You cannot change your user ID, but you can change your screen name or personalized Yahoo services.
Name change for mail:
Click "options" (top right) on your mail page, click "general preferences". In "name and e-mail" you may change which name appears in the "from" field for mails you want to send. In "reply to" changes are also possible. Make sure you save your new settings. Note: you should sign out and back in again to make sure that the settings are working.
For the messenger:
Go to your yahoo messenger friends list. Click on messenger, then click on "my contact details", underneath the box in which you could enter your first, last and middle name is a box that says nickname. Enter your new nick, save it and you're done.
If users already added you to their messenger list and/or address book, your old name setting will continue to get displayed for them. If you want those users to see your new name also, ask them to remove you from their messenger list and/or address book and add you back with your new info.
For YA:
Go to your profile by clicking on your avatar, click "edit my info", go to "nickname", mark "use another nickname", type it in the box. You have 22 characters to work with. Click "preview" and then "okay".