How can customers manage tag names via the backend in Shopify?

Hi @BayOfDenmark

can you try the below code?

{% for tag in product.tags %}
  {% if tag contains section.settings.badge_name %}
     {{ tag }} 
  {% endif %}
{% endfor %}

Also, you should define the badge_name setting in your schema block like this

{
  "type": "text",
  "id": "badge_name",
  "label": "Badge Name",
  "default": "Bestseller"
}