May left for Brussels amid bitter complaints from British police and other security forces about leaks of sensitive material related to the investigation by USA officials.
"We are shocked and saddened by the news of former Bury College student John Atkinson who sadly lost his life during Monday evening's incident", Bury College Principal Charlie Deane told CNN in a statement.
Britain's National Police Chiefs' Council warned on Wednesday that the "underauthorised disclosure" of potential evidence was a breach of trust that had potentially undermined a "major counter-terrorism investigation".
Counter-terrorism detectives have spoken in the past about how important it sometimes is that the names of suspects do not make it into the media.
"The alleged leaks coming out of government agencies are deeply troubling", Trump said in a statement the White House released. "These leaks have been going on for a long time and my administration will get to the bottom of this", Mr Trump at a summit of North Atlantic Treaty Organisation leaders in Brussels.
A British official, speaking on condition of anonymity, said police in Manchester will stop sharing information about the investigation with the USA until they get a guarantee that there will be no more leaks to the media.
Announced on Wednesday, the "Dangerous Woman" pop star postponed her concert tour as the city continues to recover.
In addition, officials in Libya said they arrested another brother, Hashem Abedi, and their father, Ramadan Abedi.
In a statement, a spokesperson for the National Counter Terrorism Policing underscored the importance of the trust between US and British law enforcement officials and said "when that trust is breached it undermines these relationships, and undermines our investigations and the confidence of victims, witnesses and their families". He said he was a Liverpool fan and I said, 'I'll stop and help you now!' It was just to help him to get him talking.
"I'm trying", he says.
British Transport Police said armed officers would start to patrol United Kingdom trains due to the increased threat of extremist attacks.
Police carried out another controlled explosion in the early hours of Thursday morning at an address in the Moss Side area of Manchester.
Saffie Roussos, 8, died in the Manchester concert terror attack. "The thought that anyone could go out to a concert and not come home is heartbreaking", Upton added.
Roussos was described as by the head teacher of the Tarleton Community Primary School as "simply a handsome little girl in every aspect of the world".
The latest victim to be named is Eilidh MacLeod, a 14-year-old from Barra in the Outer Hebrides, also died.
"Our thoughts and prayers go out to Georgina's family at this awful time, and we think especially of her brothers Harry and Daniel who were also former students of the school".