Yes , Insurance Regulatory and Development Authority is the full form for IRDA.

Headquarter of IRDA is in Hyderabad, Andhra Pradesh . It is an agency run by the government of India.

Life Insurance Product offers :
Bajaj Allianz Life Insurance Co. Ltd.
Shriram Life Insurance Co. Ltd.
AEGON Religare Life Insurance Company Limited
DHFL Pramerica Life Insurance Co. Ltd.
ICICI Prudential Life Insurance Co. Ltd
Kotak Mahindra Old Mutual Life Insurance Limited
Star Union Dai-ichi Life Insurance Company Ltd.
Exide Life Insurance Co. Ltd
Bharti AXA Life Insurance Co. Ltd.
Aviva Life Insurance Co. India Ltd.
Max Life Insurance Company Limited
PNB MetLife India Insurance Co. Ltd.
Edelweiss Tokio Life Insurance Company Limited
Canara HSBC Oriental Bank of Commerce Life Insurance Co. Ltd.
Birla Sun Life Insurance Co. Ltd
SBI Life Insurance Co. Ltd.
Tata AIA Life Insurance Company Limited
HDFC Standard Life Insurance Co. Ltd
Life Insurance Corporation of India
India First Life Insurance Company Ltd.
Reliance Life Insurance Company Limited
Future Generali India Life Insurance Co. Ltd.
Sahara India Life Insurance Co. Ltd.
IDBI Federal Life Insurance Company Ltd.