There are two entities to be kept in mind here.

The British Broadcasting Company Ltd. was a short-lived British commercial company formed on 18 October 1922 by British and American electrical companies doing business in the United Kingdom. Licensed by the British General Post Office, their original office was located on the second floor of Magnet House, the GEC buildings in London and consisted of a room and a small antechamber. On 14 December 1922, John Reith was hired to become the Managing Director of the company at that address. The company later moved its offices to the premises of the Marconi Company. The BBC as a commercial broadcasting company did not sell air time but it did carry a number of sponsored programmes paid for by British newspapers.

On 31 December 1926, the company was dissolved, and its assets were transferred to a non-commercial and crown-chartered organisation also known -- somewhat confusingly -- as the BBC; but in the case of the 1926 organisation the initials stood for "British Broadcasting Corporation." This is the organisation that is still known worldwide today.

More Info: en.wikipedia.org