When meeting new people, look them in the closest proximation of the eye as your anxiety will allow.
Smile as best you can approximate, without grimacing like you have to poop.
Say their name at least three times in the conversation, so that you remember their name.
But if you forget, there is no need to move to a new state in the dead of night. You can say, "I am sorry, but I forgot your name. Can you please tell it to me again?" Most people will forgive you for not remembering their name, unless you've been married for the past thirty years.