What is the name of the maximum mass a white dwarf can have before electron degeneracy pressure fails?

The maximum mass a white dwarf can have before electron degeneracy pressure fails is called the Chandrasekhar limit.

Subrahmanyan Chandrasekhar calculated the limit in 1930 while studying the effects of special relativity on dense electron-supported stars. Its modern value is about 1.4 times the mass of the Sun, with the exact value depending on composition and physical conditions. Below this limit, electron degeneracy pressure can support a white dwarf against gravity.

If a white dwarf approaches the limit by gaining matter from a companion or merging with another white dwarf, carbon fusion may ignite explosively in a Type Ia supernova. In other circumstances, continued collapse can lead toward a neutron star or black hole, depending on the star’s composition and evolution.

The Chandrasekhar limit applies to white dwarfs, not directly to black holes. The related Tolman–Oppenheimer–Volkoff limit concerns the maximum mass of a neutron star, supported mainly by neutron-related pressure.