Dawn theme filtering customization

Thanks so much!!

here is a preview link of our website:

https://laneh-co.myshopify.com/collections/cushions

As you can see on top of the page, it shows the filter “color” and when you select that, you see a long list of color names picked from the product specific color variant. However, the product specific color variant is the “design” name of the colors. I don’t want the color filter to pull from there. I want to define a generic list of colors and then perhaps add those generic colors as tags to each product. This way the customer can just filter by “red” or “red”/“green” together and they see all the products that have “red” or/and “green” tags.

Does that make sense?