Probably named after a Canning, but nobody is sure which one.
It is often linked to Charles John Canning, first Viceroy of India, who suppressed the Indian Rebellion of 1857. But the name was in use nine years before the rebellion, so his father, Prime Minister George Canning, may be the real dedicatee; another theory names a local firm called Canning. The station opened in 1847 as Barking Road and became Canning Town in 1873.