When you are using cPanel Roundcube webmail application, it will use your email address as email display name (sender name) by default. You can change how it displayed to your email recipient by following steps mentioned here

1. Log-in to your email (using RoundCube)

2. Click on the drop down arrow next to your email address (located at the right hand corner of webmail) and select Roundcube,

3. Click on Settings,

4. Under Settings, select Identities and choose on the email address you want to modify the disply name,

5. Enter the information in the Display Name field and click Save button,