It isn't the purpose of this site to recommend specific service providers, so I suggest you don't go there.
In any case, if I was in your position, I'd be talking to the Financial Ombudsman (FO) - not to a paid-for lawyer. Part of what the FO deals with is the power to investigate insurance companies - including where claims have been denied. The website is here:
http://www.financial-ombudsman.org.uk/about/index.html
In the first instance, and this is made clear on the website, the customer must have used a complaints procedure with the organisation in question first. If that fails, the FO might agree to take up your case - it is free to the general public.
The crux of this (I think) will boil down to whether the holding back of the information about the name change can be considered 'material' to the insurance contract - you say it isn't - the company is presumably maintaining it is.