Where they actually come from
Your business name and your logo are set once, under Settings then Brand, in Business branding. They are not on the Card Design tab and they are not per Program: every Loyalty Program you run uses the same ones, so setting them once sets them everywhere.
The only thing a single Program can have of its own is its colour, using Colour Override on its Card Design tab.
If there is no logo at all
A card with no logo uploaded shows a circle with the first letter of your business name in it. That is the fallback rather than a fault, and uploading a logo replaces it.
If it is missing in Google Wallet only
Google Wallet now shows the Brand Icon inside a white circle. White artwork on a transparent background disappears into that circle, so the logo is there but cannot be seen, and Google Wallet shows a blank white circle where your mark should be. Upload a coloured mark, or the same mark on a solid background, under Settings then Brand. This is about the Brand Icon only; the Wide Logo is not drawn in a circle.
If it shows the wrong name
Check Business name under Settings, then Brand. It is the name customers see on every card. The Loyalty Program name beside it is a different thing: it is mainly for organising your Programs, and it only appears on a customer’s card if you have ticked Show Program Name on the card front, under Card Design.
If you changed it and nothing happened
Make sure you pressed Save, and reload the page you are looking at. Cards opened in a browser show new branding at once; a pass already in a customer wallet picks it up the next time that card is stamped.
Changing your branding never touches anybody’s stamps.