All India Radio (A.I.R.) for broadcasting was named in the year

Concept — A broadcasting organisation is renamed when its ownership or administrative status changes, so its naming milestones map one-to-one onto its institutional phases: a private licensee, a state-run service, and a centrally administered national service. Dating a name therefore means dating the reorganisation that produced that name, not the date the medium itself first reached the country.

Application — Indian radio passed through exactly these phases:

1. Private phase: the Indian Broadcasting Company Ltd. was registered in 1926 as a private licensee and put its Bombay station on air on 23 July 1927, followed by Calcutta.

2. State phase: after the company went into liquidation the Government of India took the service over and ran it as the Indian State Broadcasting Service (ISBS) from 1 April 1930.

3. National phase: on 8 June 1936 the ISBS was reorganised and renamed All India Radio (A.I.R.) — this reorganisation is the naming event the question asks about, so the answer is 1936.

Cross-check — the other three years mark different milestones on the same timeline, none of them the adoption of the name All India Radio:

• 1926 — registration of the private Indian Broadcasting Company Ltd.: the start of organised broadcasting in India, not a naming of the national service.

• 1946 — the network, enlarged during the Second World War for news and publicity broadcasts, was still operating a small group of stations as a Government of India service in the run-up to Independence.

• 1956 — Akashvani was adopted as the Hindi name of the same national broadcaster: a later and separate renaming, roughly two decades after the English name.

Hence the broadcasting service was named All India Radio in 1936.