noun, noun which may take the genitive case particle 'no'
second generation; the second; junior
Refers to the second person to hold a title, position, or name in a succession, such as a business, artistic lineage, or family role. Often used with names or titles.
As the second-generation president, he expanded the company.
I attended the party celebrating the succession to the second-generation name.
初代 means 'first generation' or 'the first', while 二代目 specifically refers to the second in a succession.
三代目 means 'third generation', continuing the lineage after 二代目.
初代 is the founding first generation, while 二代目 is the successor who takes over as the second generation.
Compound of 二 (ni, 'two'), 代 (dai, 'generation'), and 目 (me, ordinal suffix). The combination straightforwardly means 'the second generation'.