Will multiple h3 tags hurt my SEO?

The Also Bought widget product names are set by default inside <h3> HTML tags.

Urban legend says that having multiple <h3> tags is bad for SEO, but that is not true.

Multiple <h3> tags are perfectly correct following the HTML5 specification and will not negatively affect SEO.

Google's opinion

You can see what Google says about repeating headers on its official YouTube channel:

Summarizing his words, it is normal to have repeated headers if they structure your store correctly.