Yes, it's possible. If you just need 1 call blocked in particular, you can press *67 before dialing the desired phone number.
If you want every call to appear as private, then I would need to enable this on my end. Please send me a private message verifying your first and last name, the phone number, street address, and the account number associated with your services.
To send a private message click on my name "ComcastChe", then click private message me.
To find out more about blocking your phone number, check out this link, Use the Caller ID Blocking Feature with XFINITY Voice.