How do I change a Themes Header Image?

If your theme supports header images, it should be under Appearance > Header. No need to replace the old file, you can simply upload a new one. If this is not the case, you can change the reference to header-new.jpg in the editor, and upload your new header to the same folder via your ftp client. You could also replace the header.jpg file but then you would lose the default one.

The recommended solution would be to create a child theme, but that’s slightly more complicated.