Log into your account, using your web browser, via Outlook.com (rather than by, say, using a mail client or an Android app).
Click on your username (top right) and then on 'Edit Profile'.
Click 'Edit'.
Change the relevant entry.
Click 'Save'.
(Note 1: If the correct name is already shown in the relevant field, change it to something random, save it, log out and then log in again to correct the entry.
Note 2: The foregoing is based upon a bit of googling. Most people around here, myself included, wouldn't touch Hotmail/Outlook with an infinite number of the proverbial bargepoles!)