This is actually more relevant than you may realize. Many people considering remembering or asking for names as extremely important, I am terrible with names at times and this can be very embarrassing if you have a sales role so I worked out effective ways to get someones name so you dont look silly
In this case I would say something " thanks for the chat the other day, I enjoyed it. Whats your name by the way, I am Malc"
This way you are recognising the conversation as relevant but you also want to introduce yourself
Well my initial concern was why she was talking to me so was off guard. Only people begging for change or psychos talk to me first