Sorry but I don’t think I understand what you want to accomplish.
Please correct me if I’m wrong:
You have two logos: one blue and one white. The blue logo is for your theme in a color palette with white background. And you want the white logo to show up with a different theme that has a color palette with a black header, correct?
For the dark mode logo to show up, you have to create the color palette from one of the dark base palettes (like Dark and WCAG Dark) then adjust the colors to your liking (black header, etc.) and assign that palette to your theme:
Also, you could configure your color palette in the site setting default dark mode color scheme id so it’s the palette used for the dark mode.