This helps others know if they have found the right person or not. When they find your public lists, they will see your name, birthday, and city if you have added that information. Anyone can search for your public lists using your name or email address.
Be aware that Amazon uses some of this information in this menu to make your list more searchable for people who come to Amazon looking for your list. You can also set a default list or delete the list altogether. When you manage a list, you can change the name, privacy settings, and description. This reveals a menu with the option to Manage list. If you want to make some changes to an Amazon Wish List, simply click on the list you want to edit.