Aer Lingus and Booking Agent both refusing to change name on ticket

Before we start, yes I know it was stupid to book with a 3rd party but here we are…

I’ve booked return flights from LHR-SNN-JFK with Aer Lingus for next month however my plans have changed and I now need to change the name of the second passenger. As this was booked through a travel agent, Aer Lingus have said through their online chat (3 times) that it must be the travel agent that requests the name change.

The travel agent in question is GoToGate. I first went on the online chat and requested the change, which they charged for, however then refunded the next day stating it was not possible and that I need to request the change myself. I have tried multiple times on the chat and called them up, even emailing them proof (screenshots from the Aer Lingus support) that Aer Lingus will not allow me to change it and it must be them.

I’m running out of ideas and not sure what to do. If you guys have any methods or experience in getting them to change the name it would e greatly appreciated.