I’m using Dawn theme and I’m wondering if I can change the logo and positioning exclusively on the password page, but no where else on the site
The Dawn theme doesn’t have the functionality to set a separate logo for just the password page (it’s coded to use the logo that you have set within your ‘brand settings’ on all parts of the site). The only way to accomplish this would be to edit the coding for the password page, to use a specific image URL for the logo.
The coding for the logo image (Dawn v13.0.1) can be found in the “main-password-header.liquid” section. You’d want to replace lines 10-20 with new coding for showing your custom password-page logo.
Here’s a help doc on how to create HTML for showing an image: https://www.w3schools.com/html/html_images.asp
If you’re unfamiliar with making custom coding edits, then you’d want to hire a custom coder from this page (https://www.shopify.com/partners/directory/services/store-setup/customize-theme), or else you can reach out to me via the contact details at the bottom of this post, and I’ll quote you for the work.
Alternatively, most premium (paid) themes, will have the ability to set a separate logo for the password page, built-in to the theme.