Why am I unable to sign up a Facebook account, because as I tried signing up, this are the instructions that appears to me. "My name is rejected or either I will hear that An unknown error occur" so what is the cause of it?
System Configuration: Android / Chrome 78.0.3904.96
Its not really clear from your mail if you already have a pre-existing account or not but if you are looking to set up a new account here are the steps you need to follow:
1)Log out from your current account
2)Go to this page 3)Fill-in all needed information, but make sure to use another email.
If however your account has been blocked, have a look at this other forum thread where other users have provided several good solutions. I should add that if your account has been blocked, you will be required to send ID to facebook to prove your identity. Information on that can be found here