Hi Sof,
Welcome to EQ! Lemme walk you through changing your name on Outlook.com:
Open Outlook.com and make sure you're logged in.
In the top right hand corner you will see your name and profile picture (if you uploaded one).
Click on your name and click "Edit Profile" You will be brought to this screen.
Next to your name click "Edit"
Enter your name here. It may not allow you to save without a last or surname but you can place something else there like your initial.
Be sure to click save after you're done.