Moses John, 14, and Pauline Watson, 46, vanished in May 2015 from their home in Northampton.
It is believed Ms Watson has links to various parts of London.
Moses, who has special educational needs, was at the centre of family court proceedings, in which children are not normally identified.
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Northamptonshire County Council, which has responsibility for Moses's welfare, said the judge, Mr Justice Michael Keehan, had agreed to disclose the identity of the boy because of the level of concern about his well-being.
Police said Moses was about 5ft 9ins (1.75m) tall, while his mother was about 5ft 7ins (1.7m) tall. The pair had a "very close relationship" and were rarely seen apart.
Police say Ms Watson has links to London boroughs including Croydon, Islington, Merton, Sutton, Southwark and Lambeth.
Speaking at the High Court, Mr Justice Keehan said: "I am gravely concerned for his welfare so long as his whereabouts, presumably in the care of his mother, remain unknown."
A teenage boy who disappeared with his mother a year ago has been named by a High Court judge in an "exceptional" attempt to trace him.