Adam Thomas, 22, and his girlfriend, Claudia Patatas, 38, were convicted of being members of the far-right organisation National Action, which was outlawed in 2016.
Birmingham Crown Court heard the pair gave their baby the middle name “Adolf”, which self-confessed racist Thomas told jurors was done in “admiration” for the leader of Nazi Germany.
A third defendant - a prominent member of National Action's Midlands chapter, Daniel Bogunovic, 27, of Leicester, was also convicted on Monday following the seven-week trial.
Thomas, described in court as a “vehement Nazi,” also faces a charge of possessing bomb-making manual The Anarchist Cookbook, which the jury is yet to reach a verdict on.
Over the course of their trial, the court was told the couple, of Banbury, Oxfordshire, met online in November 2016 before moving in together six months later.
The pair possessed a “family album”, which included photographs of Thomas dressed in white Ku Klux Klan robes cradling his newborn son named after Hitler.
Another picture in the album showed the couple smiling in a shot with their baby as Thomas clutched a Swastika flag.
The court heard they had joined National Action after being being “fuelled by hatred and division” and engaged in a “terror born out of a fanatical and tribal belief in white supremacy.”
Thomas and Patatas had both attended meetings of the organisation before it was banned in December 2016 after members celebrated the murder of Labour MP Jo Cox by a far-right terrorist earlier that year.
Despite attempts to shut National Action down, the group continued to orchestrate what it described as a “white jihad” – a holy war attempting to spread white supremacist values across the UK.
The court heard transcripts of exchanges on the encrypted messaging app Telegram, proving all three defendants remained members of the organisation after it was banned.
Portuguese-born Patatas, used the platform to message another neo-Nazi to tell him that “all Jews must be put to death”.
The former wedding photographer, who has a black sun SS symbol tattooed on her back, also said she had once celebrated Hitler’s birthday with a cake decorated with the face of the Third Reich leader.
“I did struggle to slice his face. Adolf is life,” she wrote to members of the group.
Meanwhile, Thomas authored a string of posts, calling for refugees, black people, mixed-race children and gay people to be executed.
The messages, from a chat group named “TripleK Mafia” were found by police on a mobile phone seized from National Action Midlands leader Alex Deakin, 23, from Birmingham.
When counter terror police raided Thomas and Patatas’ home they found Nazi flags, Ku Klux Klan robes and a variety of fascist memorabilia - including Swastika cushions and pastry cutters.
The couple even had racist Christmas cards - including one bearing a picture of KKK members bearing the message “May All Your Christmasses Be White”.
Barnaby Jameson QC, prosecuting, told the court earlier in the trial: “National Action is a group of vehement neo-Nazis, glorifying Hitler and the Third Reich.
“Openly and aggressively Nazi, National Action is anti-black, antisemitic, anti-Islamic and anti-gay.
“The world into which this case will take you is a world in which any right-thinking person would wish did not exist.”
Thomas, Patatas and Bogunovic will be sentenced on a date yet to be fixed.
Additional reporting by agencies