The answer is: A
Explanation
The correct option is A: Bar Council of India.
The reason is that Section 18 of the Advocates Act, 1961 provides that any person whose name is entered as an advocate on the roll of any State Bar Council may make an application in the prescribed form to the Bar Council of India for the transfer of his name from the roll of that State Bar Council to the roll of any other State Bar Council. The Bar Council of India, on receipt of such application, shall direct that the name of such person shall be removed from the roll of the first mentioned State Bar Council and entered in the roll of the other State Bar Council, without the payment of any fee. The State Bar Councils concerned shall comply with such direction.
The other options are incorrect because they are not authorized to grant the transfer of name from one State roll to another. The State Bar Council where one is enrolled or where one seeks transfer has to follow the order of the Bar Council of India and cannot decide on the transfer independently. The High Court of the state where one is enrolled has no jurisdiction over the transfer of name from one State roll to another, as it is a matter governed by the Advocates Act, 1961 and the rules made by the Bar Council of India.