I have a Google Plus Business page at: https://plus.google.com/+Clickbasics
The header (cover?) image is wrong. Apparently, as a local business, I can't change this. I'd be happy changing it from a local business to a brand in order to change the header image, but I don't want to lose the +Clickbasics as the URL.
What's my best approach?
I presume you mean the rectangular image on the right-hand side, not your portrait?
I have a Google+ page for a local business, and simply hovering over the cover image brings up a "Change cover" link. You can either choose from the default set or upload your own.
Changing the Cover Image won`t affects your URL: plus.google.com/+Clickbasics/posts It will remain same. You just need to click on change cover image.
Also I have found that there is some missing information in your business page like Tagline, Introduction, Other Social Media Links and Reviews
I don't see any link to change cover image -- a button, menu item, or hover. Please see attached screen shot. Please point out anything I'm not seeing.
In the top left-hand corner of that screen is a drop-down menu which says "My Business". Use that menu to select "Google+" or whatever the next option down on the list is called. You can change the photo from there, as I described before.
That worked! Many thanks.