Diagnosed shortly after birth with the rare genetic disorder, 11-month-old Charlie has spent the last nine months on life support at the London hospital.
Mr Justice Francis had made an order barring journalists from naming Dr Hirano or saying where he was based early this year.
The European Court of Human Rights rejected an appeal from the parents, which briefly stalled their legal options.
If he concludes that Charlie could be treatable, his parents will be hoping that they can overturn the current court ban on them taking their 11-month-old son to the United States for treatment by Dr Hirano.
British doctors determination to end Charlie's life, even though hospitals in both the USA and the Vatican have offered to take him and his parents have raised over £1.3 million in public donations to handle the necessary logistics themselves, has proved controversial around the world.
Two hours into the High Court hearing, questions from Judge Nicholas Francis prompted tensions to boil over.
He is due to stage further hearings later this month following next week's gathering of specialists.
Dr Hirano withdrew his request for anonymity when he heard it would be opposed by the Press Association news agency and other reporters.
The judge in the Charlie Gard case has ordered little boy's head to be measured to determine if there is any brain development.
The doctor estimated that there could be a 10% chance of improvement in muscle strength and a "small but significant" improvement in brain function.
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The clinicians' meeting will be recorded and a transcript will be sent to the judge, Mr Justice Francis.
The UK High Court agreed to rehear Gard's case when two global hospitals came forward with new evidence supporting the idea that nucleoside bypass therapy would not simply prolong Gard's life, but actually help him.
A number of specialists involved in the current High Court hearing are set to meet next week for a detailed discussion over his condition.
"Although Charlie's parents have parental responsibility, overriding control is by law vested in the court exercising its independent and objective judgment in the child's best interests", the hospital wrote.
Father Frank Pavone, with Priests for Life told CBN News in statement: "News that an American doctor with experience in treating Charlie's disease will travel to the U.K.to examine him is certainly welcome".
Lawyers representing Charlie's parents objected to the meeting being staged in the absence of both parents.
Mr Justice Francis ruled Dr Hirano, a professor of neurology at the Columbia University Medical Center in NY, could be named in media reports.
He said: "We absolutely abhor any suggestion of any threats or intimidation against members of the judiciary, legal profession or medical profession". He's now on a ventilator from which Great Ormond Street Hospital officials want to remove him against his parents' wishes.
"We are delighted that Charlie'smother, Connie, will be present at the meeting that Prof".