On the digital end, it's due diligence to check if a name has been used previously if they intend to stand out.
Some people want to blend in and use a discrete name that won't come up easily on Google.
Some people probably never thought about it, were excited about the name, and just used it regardless.
Whatever the intention, the onus is on the client to make sure who is being talked about is the correct person. I understand this is a lot more difficult when all you've got is fully in text-form only though. I see nothing wrong with it as long as they are their own real person and intend to provide the agreed upon services 🌹