The best way to have tailored experience is to make people to sign in to the site. Once they are logged in, you can store whatever information in the DB and retrieve it when needed.
If you do not want to ask for more than a name, you can generate a wordpress user for them with some dummy email and password and set the authentication cookies to have long expiry time, but this might not be ideal, very much depends on what is exactly that you want to do.
You can try to use cookies, but that will work only for a relatively shorter time period and might cause problems when you will want to server cached pages.