When I send email to others, it shows my name on that person email as the sender's nameof that email. How can I change that display name?

You can change the FROM name and the REPLY TO address on the Yahoo Mail "Accounts" page (or Advanced Options in Basic Mail). The FROM name can be blank and then only the email address will appear. The REPLY TO address can also be blank if you want it the same as the FROM address.

In Full Featured Mail:
Hover over the gear icon ⚙ to the right of your avatar and ID on the mail page.
Click "settings" and then "Accounts" in the left column.
Click "edit".
You can change the name or reply to address there.

In Basic Mail:
Select "Options" from the drop down menu in the upper right.
Select "Advanced Options" in left column.
You can change the name or reply to address there.