During the finetuning, we feed the concatenation of the persona and the conversation to the model. You can read the detail here 🦄 How to build a State-of-the-Art Conversational AI with Transfer Learning | by Thomas Wolf | HuggingFace | Medium 2
For simplicity, I finetuned my gpt2 model using simpletransformers Conversational AI Specifics - Simple Transformers 1