You could try using their contact form here and give as much evidence as you can about the name change, i.e. link to their website, info from Companies House if they're a Ltd company and any other authoritative citations where you've managed to change the name. Then keep your fingers crossed that they eventually get to it!
New advertising option:
A review of your product or service posted by a Sterling Sky employee. This will also be shared on the Sterling Sky & LSF Twitter accounts, our Facebook group, LinkedIn, and both newsletters.