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Thank you for bringing the question to the forum. This will not likely be the answer your client is hoping to hear, but they should likely rebrand. If an authoritative recruitment agency in a major city is already dominant for this brand, your client made a branding mistake. Without knowing all of your client's particular circumstances, my best advice is that it would likely be much better for them to cut their losses now and rebrand (after carefully researching whether their new name is truly unique) rather than committing to spending all of their future years in business at such a huge disadvantage. They could also possibly end up in court if the competitor decides they are infringing on their trademark. While there's a small possibility that, with enough money, your client could try to surpass the online authority of its competitor, it's not a fight I would choose to take on, because it's based on a mistake that should have been caught before the client named its company. Fighting on the basis of a mistake is a waste of time and resources that could be better spent building up the unique brand in the coming years. If the client does choose to rebrand, advise them to choose a completely different brand name, so as not to get caught up in further confusion with their former brand or their competitor.

What a great idea! I'll definitely schedule in some time with the client to ask those questions. Thanks so much!