Adam Thomas, 22, and Claudia Patatas, 38, were found guilty of being members of the extreme right-wing organisation National Action, which was banned in 2016.
A jury at Birmingham Crown Court was told the couple, of Waltham Gardens, Banbury, Oxfordshire, had given their child the middle name Adolf, which Thomas said was in "admiration" of Hitler.
Photographs recovered from their home also showed Thomas cradling his newborn son while wearing the hooded white robes of a Ku Klux Klansman.
Former Amazon security guard Thomas, formerly of Erdington in Birmingham, and Patatas, a photographer originally from Portugal, were found guilty after a seven-week trial at Birmingham Crown Court.
A third defendant, Daniel Bogunovic, of Crown Hills Rise, Leicester, was also convicted of being a member.
The warehouse worker was a leading figure in National Action's Midlands chapter.
Jurors were told Bogunovic already had a conviction from earlier this year for stirring up racial hatred after being part of a group that plastered Aston University, in Birmingham, with the group's offensive stickers.
Thomas, a twice-failed Army applicant, was also convicted of having a terrorist manual, namely the Anarchist's Cookbook, which contained instructions on making "viable" bombs.
The Crown's case was that after being banned by the Government in December 2016, National Action simply "shed one skin for another" and "rebranded".
Jurors heard evidence of social media chats involving Thomas, Patatas and Bogunovic, discussing what prosecutors have alleged was the banned group's continuing operation, under a different name.
The jury also heard that Thomas and Patatas plastered National Action stickers in public locations after the ban, while Bogunovic was calling for a "leadership" meeting in a chat group for senior members in April 2017.
Three other men who had been due to stand trial alongside the trio, admitted being National Action members before the trial began.
Thomas's close friend Darren Fletcher, 28, of Kitchen Lane, Wednesfield, West Midlands, Joel Wilmore, 24, of Bramhall Road, Stockport, Greater Manchester, and Nathan Pryke, 26, of Dartford Road, March, Cambridgeshire, will be sentenced later.