calling your family 'the Smiths' works better. if you use it in a sentence, for example
'this is my family, we are known as the Smiths'
it makes sense as you are referring to them as a group of people. if you said 'this is my family, we are known as Smiths', it is not correct and can cause confusion as some names have multiple meanings, e.g. 'Smith' is a job title and a name. When you talk about a family name this way, use 'the' to refer to the members as a collection.
Here are some examples:
If your family surname was 'Kim', you could say 'This is my family,
and together we are the Kims'
If you had neighbours with the surname 'Taylor' you could say 'The Taylors live next door'
hope that helps a bit