No.
You don’t need to reveal any kind of personal information about yourself on the Fediverse. Use any name you want, and any picture (or no picture at all).
The only information you need to give when signing up on a Fediverse server is an email address, and you can use an email alias if you want to keep it secret. The only other data a Fedi server might see is your computer’s or phone’s IP address, but this is hidden if you’re using a VPN or Tor.
Revealing personal information on the internet is a bad idea in general, as it makes unwanted tracking and identity theft much more likely.