When you sign up, FreeBusy automatically pulls the display name from your Exchange/Google account or your corporate directory.
FreeBusy will show that display name on the FreeBusy page associated with the respective calendar email. If you have multiple calendar accounts linked, you can set a distinct display name for each one.
To customize your display name:
Go to the Profile page.
Customize your display name as desired.
Click Save to persist changes.
After saving changes, FreeBusy will show your custom display name to anyone checking your availability on FreeBusy.