Google shows the domain the login redirects to, and with Supabase that's your project's supabase.co address (Google → Supabase → your app). Two ways to change it:
- Brand verification in Google Cloud Console → OAuth consent screen / Branding: app name, logo, your homepage, privacy policy and terms links, and your own domain verified in Search Console. After Google approves the branding, the account chooser shows your app name instead of the raw domain. Takes a few days, costs nothing.
- Custom domain for Supabase Auth (e.g.
auth.yourbakery.com), a paid add-on on Supabase. Then even the domain shown is yours. You'll need to add the new callback URL to Google too.
For a small shop, do 1 first. Most people only care that they see a name they recognize.