The contact you have on your Messenger list will see your name displayed as it was when you originally added them. In other words, if you added a contact to your list a month ago and you didn't realize that at that time your Contact Details were set to your real name, then they will have your real name as the Contact Details they have saved for you.

Changing your Contact Details will not change what they've saved. Once you're on someone's list, the only person that can change what they see on their list is them.

Just as you can change the Contact Details of any contact on your list, they can change your contact details on theirs and it will not affect anything other than their personal contact list. If you want them to see a specific name or nickname when they receive an IM from you, you can send them the Contact Details that you want them to see.

Here's how you can do that:

1. Click Actions on the main Messenger window.
2. Click Send My Contact Details.
3. You'll then need to select the people from your friends list. These contacts will receive your information.
4. Click Next.
5. Check the box against the piece of information you want to send. If you want to change something before sending, click Edit My Contact Details on the lower right corner of this window.
6. Click Finish.

The users you send to will then have the choice to accept or decline the Contact Details.

Any contacts you add to your list will see the new contact details that you've set for yourself. Anyone that you contact that is NOT on your list will see only your Yahoo! ID until you add them to your list and then they'll see what you've set for your Contact Details.