No-name insurance companies

[Nabeel M.]

Hey Team,

We all know the better known property insurance companies; Allstate, GEICO, etc.  Having said that there are a series of lesser known insurance companies.  Some are part of a larger holding company (e.g. Berkshire Hathaway) sometimes not.  Assuming a "no-name" or lesser known company has a strong AM Best Rating are they as likely to approve a claim as a better known company?  I understand AM Best speaks to a company's financial strength but how to think about lesser known companies and their propensity to pay out?

Thanks in advance for your thoughts.