Question: My father insured his own life and named me as nominee. After his death, does the insurer have to pay me directly?
Answer: Yes, if the nomination is valid and the policy terms are met, the nominee is beneficially entitled to the amount payable under Section 39.

Supporting evidence:
title: noc.irdai.gov.in/Insurance%20Act,1938%20-%20incorporating%20all%20amendments%20till%2020212021-08-12.pdf
quote: where the holder of a policy of insurance on his own life nominates his parents, or his spouse, or his children, or his spouse and children, or any of them, the nominee or nominees shall be beneficially entitled to the amount payable by the insurer to him or them under sub-section ( 6 )
context: than one, all the nominees die before the policy matures for payment, the amount secured by the policy shall be payable to the policyholder or his heirs or legal representatives or the holder of a succession certificate, as the case may be.
(6) Where the nominee or if there are more nominees than one, a nominee or nominees survive the person whose life is insured, the amount secured by the policy shall be payable to such survivor or survivors.

ASSGNMENT OR TRANSFER OF POLICIES AND NOMINATIONS

(7) Subject to the other provisions of this section, where the holder of a policy of insurance on his own life nominates his parents, or his spouse, or his children, or his spouse and children, or any of them, the nominee or nominees shall be beneficially entitled to the amount payable by the insurer to him or them under sub-section ( 6 ) unless it is proved that the holder of the policy, having regard to the nature of his title to the policy, could not have conferred any such beneficial title on the nominee.
(8) Subject as aforesaid, where the nominee, or if there are more nominees than one, a nominee or nominees, to whom sub-section ( 7 ) applies, die after the person whose life is insured but before the amount secured by the policy is paid, the amount secured by the policy, or so much of the amount secured by the policy as represents the share of the nominee or nominees so dying (as the case may be), shall be payable to the heirs or legal representatives of the nominee or nominees or the holder of a succession certificate, as the case may be, and they shall be beneficially entitled to such amount.
(9) Nothing in sub-sections ( 7 ) and ( 8 ) shall operate to destroy or impede the right of any creditor to be paid out of the proceeds of any policy of life insurance.
(10) The provisions of sub-sections ( 7 ) and ( 8 ) shall apply to all policies of life insurance maturing for payment after the commencement of the Insurance Laws (Amendment) Act, 2015 (5 of 2015).
(11) Where a policyholder dies after the maturity of the policy but the proceeds and benefit of his policy has not been made to him because of his death, in such a case, his nominee shall be entitled to the proceeds and benefit of his policy.
(12) The provisions of this section shall not apply to any policy of life insurance to which section 6 of the Married Women's Property Act, 1874 (3 of 1874), applies or has at any time applied:

ASSGNMENT OR TRANSFER OF POLICIES AND NOMINATIONS