I’ve come in contact with that group or a group very similar. I don’t think the one I was talking to had an actual name, but they claimed to be the true church of Christ and renounced all other Christian faith traditions.
They don’t consider themselves Protestant because they never broke away from the Catholic Church – they were never a part of it in the first place.
Some Baptist churches say the same thing as do some of the independant, free, Bible churches. They say they are not Protestant’s because they were never a part of the Catholic Church to begin with and they are just Christian. No other name than Christian.