This company (in Singapore) calls it a "backpack cooler" and then, in the blurb, says: We have created this insulated backpack so that you can carry the food and drink you need and keep them cool for half a day. Super-convenient for your walks! Our motivation? You no longer have to choose between a backpack and a cooler. Now you have 2 in 1! The volume of this bag is 10 litres.
On amazon.uk similar items appear to be called variations of 'cool/cooler/insulated/bag/rucksack.'
This one covers all eventualities in its description: "Large Capacity Cool Bag Rucksack Lightweight Cooler Bag Backpack Insulated Rucksack Hiking Picnic Daypack for Men Women to Camping, Sports, Beach, Work, Family Trip"
And then, in their blurb, they seem to settle on 'cool bag rucksack: Padded, adjustable cool bag rucksack straps comfortably to your back, leaving both arms free to grab your surfboard, fishing pole or any other gear your adventure calls for.
In the U.S., a cooler is generally a rigid plastic insulated box with a lid, and usually a handle/handles, that is used to keep things cool by including ice or frozen reusable ice packs. (Like the one in the middle.)
I would call the one on the right an insulated backpack (which serves as a cooler, but I wouldn't call it that).
The one on the left I might call a soft-sided picnic basket/carrier. I can't tell if it's insulated.
I'd call all of these things coolers, assuming that the one on the left is insulated. I'd qualify the one on the right with 'backpack' (backpack cooler).
Exactly opposite to Andygc's approach, I'd call most things that passively keep things cool coolers.