The kidney was intended for another patient listed higher on the transplant matching list. Photo: Virtua Health

The transplant was intended for another person with the same name and of a similar age.

Virtua Our Lady of Lourdes Hospital in Camden said both patients have now received transplants and are doing well.

The mistake was discovered a day after the transplant procedure. The hospital called it an "unprecedented event".

"Mistakes of this magnitude are rare," Reginald Blaber, executive vice president and chief clinical officer at Virtua Health, said in the statement. "And despite the unusual circumstances of similar patient identities, additional verification would have prevented this error."

A member of the hospital's clinical team realised a day after the first transplant on 18 November that the 51 year old received the kidney out of priority order, as they were lower on the transplant matching list, which is managed by the United Network for Organ Sharing.

About 113,000 people are on a waiting list for an organ transplant, with nearly 95,000 of them waiting for kidneys, according to the organisation's website.

The patient who was supposed to receive the initial kidney received another one about a week later.

The hospital has not identified the patients.

Mr Blaber also said: "As an organisation committed to safety and process, we immediately instituted additional measures and educational reinforcement to help ensure this does not happen again."

Virtua Our Lady of Lourdes Hospital is the only facility in southern New Jersey to provide kidney, liver and pancreas transplants, according to their website.