I changed my logo but the shop products do not show it?

Short answer: This is normal: a live shop is never modified directly. Open a draft, check how it looks, then put it into service.

Cause

Your logos live in the “My logos” tab, independently of your shops. Replacing a logo's file therefore updates the logo, not the shops that are already online: those keep showing whatever was last put into service.

This is not a display delay, and there is no cache to clear: nothing goes online until you decide it does.

How to spot it

On the shop concerned, an orange banner warns that logos have changed, and the products using the modified logo are themselves marked with an orange background. As long as that banner is there, the live shop is showing the old logo.

Solution

On the “Shops” page, select the shop concerned in the left-hand panel.
Click the orange “Modify the shop (create a draft)” button. The system creates a working copy — the draft — and that is what receives the new logo. If a draft already exists, open it instead of creating another one.
Click the green button at the top right to have the draft's website built — its tooltip reads “Create the website of this draft shop to see all changes”. You can then look at the result: the draft's address carries a _draft suffix, so you can view it without touching the live shop.
When you are happy with the result, click “Put this draft shop into service” (blue button with two checkmarks). The draft replaces the live shop, new logo included, and the orange banner disappears.

This step is not pointless red tape: it is what lets you check how the new logo looks on your products before your buyers see it. A logo replaced in the wrong format, or on the wrong background, gets caught on the draft rather than on your orders.

Going further

I have received my real logo, how do I replace it — replacing the file inside the existing logo instead of creating a new one.
How do I put my logo in my shop header — the same trip through a draft, for the header logo.