I would paint a label area to write the name, with chalkboard paint. But, first I would paint it green and decorate it !like a little Christmas tree. Turn it upside down after painting it green and glue a star or Angel on top. Leave it right side up and you could put an ornament or small plant in it. Or fill it with candy.
Paula, Here is one that was made for Thanksgiving, but perhaps you could adapt it to a snowman hat? I'd paint them black and put the names on the hats in a light color. Hope this helps you.
While this is Thanksgiving, I think you could adapt it to be bells or ornaments. https://www.hometalk.com/24316749/terra-cotta-thanksgiving-hats
If you are using terra cotta pots, you can:
Here is a fun post with a bunch of different ideas that you can add a name to for a place card. Some are using larger pots but just scale them down to a small size. Have fun! http://diyandcrafting.com/clay-pot-christmas-craft-ideas/