In short: financial regulators are the institutions that admit financial firms to the market, check that they follow the rules and receive complaints — typically a central bank or banking supervisor, a supervisor for the non-bank sector, a consumer authority and a data protection authority.
Simply put: Each "referee" guards a different field. Knowing whom to turn to saves time. Their registers show whether a firm may operate. At EU level the ECB supervises the large banks in the euro area, while the EBA, ESMA and EIOPA set common rules and issue warnings.
Example: An insurer refuses a claim without explanation. That is not for the central bank but for the insurance supervisor.
Watch out: a licence means the firm is supervised, not that profit is guaranteed.
Example: Bulgaria — BNB: banks, payments, register of non-bank lenders; FSC: insurance, investment firms and funds, pensions; CPC: consumer rights and the Conciliation Committee for Payment Disputes; CPDP: personal data.
Check in your country — your central bank and financial supervisor's public registers.
Source: BNB — Banking supervision: https://www.bnb.bg/BankSupervision/index.htm · FSC: https://www.fsc.bg · CPC: https://kzp.bg · CPDP: https://cpdp.bg