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.
What if I want to impersonate someone else?
Whatever name you choose to use, don’t impersonate other people, it’s not very nice and would break the rules on many servers, possibly getting you banned. Impersonation may also be illegal in some countries.
Can I leave the profile picture blank?
Yes, if you want. A lot of blind people on the Fediverse don’t use profile pictures, and there is no obligation to have a picture.