What is the name of the first black hole confirmed to exist?

The first black hole widely accepted as confirmed to exist was Cygnus X-1.

Cygnus X-1 is an X-ray source in the constellation Cygnus, roughly 6,000 light-years away. It is part of a binary system with a blue supergiant star. The unseen companion pulls gas from that star; as the gas spirals inward, it becomes extremely hot and produces powerful X-rays.

Astronomers discovered the source during a 1964 rocket flight. Measurements of the companion's orbit showed that the compact object was far too massive to be a neutron star or an ordinary star. By the early 1970s, Cygnus X-1 was generally regarded as the first strong black-hole candidate, and later observations strengthened the case.

The phrase “first confirmed” is a convenient quiz shorthand: astronomers cannot observe a black hole directly, so the evidence is based on its mass, compactness, and effects on nearby matter. Cygnus X-1 also became famous through a 1975 wager between Stephen Hawking and Kip Thorne. Hawking bet against it being a black hole, then conceded in 1990 as the evidence became more compelling.