How does street naming work there?

When street names are mentioned in American media, almost all the time, it'll be something like "on 23rd Street" or "The corner of third and eighth."

Do American streets not get named anything other than numbers? An example, here in New Zealand, we've got a whole range of Street/Lane/Quay/Drive/Ave names, such as: 'Smith' Street, 'Gloucester' Street, 'Park' Drive. Do American suburbs strictly stick to numbers, or does the media I consume just make it seem like that?