While you are not able to remove your name from your profile, you can choose a new nickname.
If you're on a computer, locate the dropdown menu in the upper-right-hand corner of YouNow and select "Settings." Change your nickname and hit "Save." If you'd like to replace your profile name with your nickname, check the box below the "Nickname" section.
If you are on a mobile device, tap the avatar icon of your YouNow app's tool bar. From here, tap the gear icon --> "Edit Profile" --> double tap on your "Nickname & URL," and edit your nickname.