Change the "From:" Field - Hotmail

Microsoft Account Setup

The old versions of Hotmail kept separate credentials for each user. The service, which superseded Hotmail, is tied to a Microsoft Account.

To change the display name for your email account — using a or an address — you'll need to change it for your Microsoft Account by editing your profile page.

Log in to your Microsoft Account Profile page then just click Edit name below your display name. Change your name, solve the CAPTCHA, then save. This change will propagate to all accounts (not just email) federated with your Microsoft Account.