When asked again what his name was, Mair calmly repeated: "My name is death to traitors, freedom for Britain."
Cox, an ardent supporter of EU membership, was shot and stabbed in the street in her electoral district in northern England last Thursday.
Wearing a gray sweat shirt and trousers and flanked by two security guards, 52-year-old Thomas Mair was asked his name by a clerk at Westminster Magistrates' Court in London.
"Death to traitors, freedom for Britain," Mair said. When asked again what his name was, Mair calmly repeated: "My name is death to traitors, freedom for Britain."
Mair, balding with a gray goatee beard, made no further comment in the 15-mintue hearing, his first appearance in public since police arrested him in the town of Birstall, Yorkshire, where Cox was killed.
He is charged with murder, causing grievous bodily harm, and possession of a firearm and a knife. He was remanded in custody and will appear at London's Old Bailey court on Monday.
The killing has shocked the nation and both sides in the referendum have temporarily suspended campaigning ahead of Thursday's vote, which has far reaching implications for both the EU and Britain.
A British exit from the EU would rock the bloc - already shaken by differences over migration and the future of the euro zone - by ripping away its second-largest economy, one of its top two military powers and by far its richest financial center.
Pro-Europeans, including former prime ministers Tony Blair and John Major, have warned that an exit could also trigger the break-up of the United Kingdom by prompting another Scottish independence vote if England pulled Scotland out of the EU.