Search & Discovery color filter lists every variant name

[RoseBags]

Hello,
an example Backpack has the variants: Black, Red and Forrest     |These are the product/color names of the munufacturer and Forrest shouldn't be changed to green.
The goal is to assign these variants only a few base colors to keep the filter small.
Search & Discovery is filtering by the variant names(Forrest, Dune... the manufacturer color).

This results in 600+ color filter categories (see screenshot).

All the blank boxes on the left are these variant names.
As you can also see, I filtered for black, but also got other color results.
This is because the color black is a variant, available for this product but the default image is a different one.
It would be great if someone knows a solution for this, like an app.

Thanks for your help.