I would not be so concerned about the branding of the policy you have been taken, it is far more important to have trust in the companies that are underwriting the policy as it will be these companies that you will deal with in the event of a claim. If they are the normal Legal & General's or Aviva's or the Zurich's type companies...big brand names then you are likely to be in safe hands for your policy. If you are not aware of the company underwriting then do a google and see what type of customer reviews they have and act accordingly
It is not uncommon for a company to brand another insurance companies policies, after all, if you take out your home and contents insurance through any bank it will always be underwritten by a big name company but it will always be branded under the banks name and unless you read the documentation closely (which you really should do anyway) then you probably won't even know who is underwritting the case.
If you have any concerns over the policy or the brand or features of the policy still then the easiest option would be to cancel the policy and take out a new policy with a brand name that you hold more faith in.