Allow your customers to register and login the store using their username. Customers can create username of their choice or they can select one from the suggestions shown to them on the basis of their first name, last name & date of birth.
https://addons.prestashop.com/en/social-login-connect/45638-login-by-username.html
https://addons.prestashop.com/en/social-login-connect/45638-login-by-username.html