Michael Adebolajo, 28, from Romford, Essex, was appearing at Westminster Magistrates’ Court to face various charges.
He is accused of murdering Drummer Rigby, 25, near Woolwich barracks in south-east London on 22 May.
The significance of the name change was not explained, although Abu Hamza is an alias used by a number of Islamic fundamentalist leaders.
His co-accused, Michael Adebowale, 22, was at the same court last week and appeared at the Old Bailey yesterday.
As well as the murder charge, Adebolajo is accused of the attempted murder of two police officers and possession of a firearm, a 9.4mm KNIL model 91 revolver.
Wearing a white T-shirt and white trousers, Adebolajo blew a kiss to a man in the public gallery, and they both pointed to the sky.
Adebolajo’s left arm was fully bandaged and he held a copy of the Koran. As he was asked to stand, he did so, but asked: “May I ask why? May I ask why?” When told it was customary to stand, he said: “I want to sit.”
Adebolajo, who was referred to as Mujaahid Abu Hamza in court following his request, was charged with the four counts on Saturday, having been discharged from hospital on Friday. He was shot by police and spent just over a week in hospital.
After standing when asked to at the end of yesterday’s short hearing, he asked Deputy Chief Magistrate Emma Arbuthnot: “May I respond to you? You would prefer me not to speak to you. I am only a man. I would like to alleviate the pain if I may.”
He then kissed the Koran and raised his arm into the air.
Adebolajo was remanded in custody to appear at the Old Bailey within 48 hours for a bail hearing.
The man to whom he had gestured in the public gallery would not speak to journalists when approached outside the court.
Adebowale, from Greenwich, later appeared via video-link at the Old Bailey.
He is also accused of murdering Drummer Rigby, as well as possession of a firearm.
No application for bail was made during his brief hearing.
The judge, Mr Justice Sweeney, told the court the defendant would reappear for a preliminary hearing on 28 June, when his case is expected to be joined with that of Adebolajo.
Anti-Muslim abuse ‘peaked the day after soldier’s death’
Anti-Muslim activity reported in the wake of Drummer Lee Rigby’s death was mainly online abuse which peaked on the day after the brutal killing, police chiefs have said.
The Association of Chief Police Officers (Acpo) said 71 incidents were reported to its national community tension team (NCTT) over five days after Drummer Rigby was hacked to death in Woolwich, south-east London, on 22 May.
Detective Chief Superintendent Steve Cotter, Acpo’s lead on national community tension, said that although exact figures were “unclear”, the number of incidents appeared to have fallen. “The numbers of hate crimes did peak and they are now reducing,” he said.
“In the main, the ones that have been quoted are online… it’s people’s opinions that people categorise as unpalatable.”
Speaking at a briefing at Acpo’s headquarters in central London, Mr Cotter confirmed a small percentage of the reported incidents were attacks on mosques and claims that Muslim women were having their head scarves removed.
True Vision, an online hate-crime reporting tool operated by Acpo, received 136 reports of anti-Muslim activity – internet or physical – via its website in the week after the Woolwich attack. The number of complaints peaked on the day after the killing, an Acpo spokesman said.
Tell Mama, the charity which monitors anti-Muslim incidents, said it received more than 150 reports of anti-Muslim activity in the days after Drummer Rigby’s death, compared with an average of four to eight incidents a day beforehand.
Anti-extremism task force meets
A task force for tackling radicalisation set up by the Prime Minister in the wake of soldier Lee Rigby’s murder is to meet monthly in a bid to deal with extremism head on, a Downing Street spokesman has said.
As the two men suspected of killing Drummer Rigby appeared in separate courts, David Cameron and senior cabinet members including Deputy Prime Minister Nick Clegg and Home Secretary Theresa May gathered for the group’s first meeting.
The PM asked Education Secretary Michael Gove and Schools Minister David Laws to look at confronting extreme views in schools and charities, the Number 10 spokesman said, while Business Secretary Vince Cable is to monitor universities.
Mr Cameron also asked Justice Secretary Chris Grayling to look into similar issues in prisons and Faith and Communities minister Baroness Warsi to examine work in communities.
Other politicians in attendance were Chancellor George Osborne and Government Policy Minister Oliver Letwin.
The anti-terrorism group, which is to hear from experts at subsequent meetings, will focus on radical preachers who target potential recruits in jails, schools, colleges and mosques.
It will monitor trends in radicalisation and tackle “poisonous narratives”, No 10 previously said.
The update came ahead of an address to the House of Commons by the Prime Minister.
Drummer Rigby was hacked to death near Woolwich Barracks in south east London as he strolled back to base on May 22.
People across the country subsequently paid their respects to Drummer Rigby, with floral tributes marking the scene of his death.
But this weekend also saw clashes between rival protesters outside the Palace of Westminster, despite pleas from police and the soldier’s family not to use the death for political gain.
Around 300 Unite Against Fascism (UAF) members gathered in Parliament Square on Saturday to block the British National Party (BNP) from marching to the Cenotaph.
Fierce shouting from both sides spilled into violence and dozens of police were required to break up the disorder.
Scotland Yard said 58 people from the UAF protest were arrested under section 14 of the Public Order Act after they refused to move to their pre-arranged protest pen in Whitehall.
Protests by the Scottish Defence League (SDL) and anti-racism campaigners took place in Edinburgh’s Old Town.
The SDL held a static protest outside the Scottish Parliament, while the UAF organised its own counter-protest.
Small groups of EDL supporters gathered across England, including in Sheffield, Brighton, Luton, Colchester and Walsall.
Mr Cameron said: “It’s important that we learn the lessons of what happened in Woolwich.”
He said the Intelligence and Security Committee would investigate how the Woolwich suspects were radicalised, what was known about them, whether more could have been done to stop them and further lessons to be learned.
The committee, chaired by Sir Malcom Rifkind MP, hopes to conclude its work by the end of the year, he said.
The Prime Minister said: “To tackle the threat of extremism, we must understand its root causes. Those who carried out this callous and abhorrent crime sought to justify their actions by extremist ideology that perverts and warps Islam to create a culture of victimhood and justify violence.
“We must confront this ideology in all its forms.”