Dan and Mandy Sheldon went to register the tot last week after the council office finally opened after lockdown.
Furious Dan, 37, a plant hire company boss, lodged an official complaint over how he and Mandy, 32, were treated at their local office in Chesterfield, Derbys.
He said: "We were really excited to go and get him registered but the woman looked at us in utter disgust.
"She told us he would never be able to get a job, and that teachers wouldn't want to teach him.
"I tried to explain that we are not religious people, and Lucifer in Greek means 'light-bringer' and 'morning' but she wouldn't listen.
"She even told us that it was illegal to name a child that in New Zealand and that maybe we could name him something else but refer to him as Lucifer at home."
The parents were told to leave the room while the official checked if she was allowed to register the boy with the Satanic title.
Dan added: "We were gobsmacked with her behaviour.
"Eventually she did it, but it was through gritted teeth.