You can use a different image for each language; the code automatically uses the image that matches the current language in the shop. When the customer has selected Italian, the code will look for a file in /includes/templates/your_template/buttons/italian/.

To find the name of any sidebox, you can do a view source and look at the HTML that is being output. For Categories, look for the set of category links in the code, and note at the top of that list:
<div id="categories">

The id stays the same no matter the language in use, so you would use the same filename for images in any language. They should be saved in the appropriate language folder in /buttons/.