As others have said I wouldn't memorise them. First names are easier. But both first names and last names can vary in spelling. Such as Jeni and Jenny. And Nicky, Nikki, Nicki. Really, even we ask people how they spell their name if it can vary. Surnames can have very complicated spelling or pronunciation. As you come across names, just learn it that way. And maybe you can look up the top ten baby names so the ten most common ones are learned if it will help you.

Nothing to worry about. Learn the first names, they are simpler. Last names can be a lot more complex. For example a Greek-American name could be George Charalambopoulos. First name easy, last name ... not so easy. I am sure that there are a lot of harder names than this. So nothing to worry. If the person has a really difficult last name, it would be beneficial for both to spell it out for you anyway.

* to memorise a list of surnames...

I agree with Chris that I don't think it would be the best use of your time to a memorise list of surnames. The problem here is maybe that you don't trust your listening skills enough? But as your listening improves you will likely be better able to guess what the name is if you don't know it. This happens sometimes with native speakers too, sometimes we have to say 'wait a minute, how do you spell that? if someone has a more obscure surname, or an unusual first name.

I don't think it's essential to learn surnames there are so many I think it would be time wasted. But you could familiarise yourself with some of the most common first names, but I would not worry about it you will learn them as you go :)