When you're in your mail account, there should be a toolbar toward the top of the page. If you are still using Classic, then the toolbar will be top right, but if you're using the new Yahoo mail it will be top left. The Options link on that toolbar has a drop down menu. Click "Mail Options" from the drop down menu. This will bring up a new page with a box full of sections on the left. Click on "Accounts" in that box, and then "Yahoo! Mail" under Accounts in the new center column that comes up. This should bring up a new box titled "Sending Mail" and the second field in that box should be Your 'From' name; changing that and then clicking the "Save Changes" icon at the top will change the name that appears when you send mail.
P.S. If you've got a Yahoo profile, you'll want to change your name there too!