You can configure the first name, the last name and the nickname by clicking on the Messenger menu   My Contact Details.

Please keep in mind that entering a nickname in its special box, no matter if you also write a first or a last name, will display only this field in your contacts’ lists. Also, remember that you cannot change the way you appear in other lists because your contacts are able to modify your name as they want.

Note that if you IM with someone not on your friends list, that person will only see your Yahoo! ID