What is most important is if your business works (gets traction/clients). The name and branding is only secondary. Explain to the other company that you agree

What is most important is if your business works (gets traction/clients). The name and branding is only secondary. Explain to the other company that you agree and will change your name shortly. Start thinking of a new name and get some more clients to get some cash. If you have a good business, than it can also work without a name. It is sad to have wasted so much money just because of the name. But look for marketing solutions where you don't need to pay anything. If you already had some clients, propose some advantages if they get you more clients. etc.