They could:
1. Set up a content filter that filters op's name from the output. OpenAI would still need to keep record of the name, exposing it to leaks.
2. Remove the name from the dataset and retrain the model, which is obviously infeasible with each GDPR request.
I expect there are other instances where it is impractical or impossible to completely forget someone's data upon a request. Does Google send people spelunking into cold storage archives and actually destroy tapes (while migrating the data that is not supposed to be erased) every time they receive a request?