I don't see which model generated each request, where exactly do you see this?

I see it on the 'My Activity' page: https://myactivity.google.com/u/1/product/bard?utm_source=ba...

Here's a screenshot: https://imgur.com/a/sgtVt2O

Mine says "Bard" where yours says LaMDA. https://i.imgur.com/p8wIPHj.png

It just says "Bard", even if I click on "Details". Are you, perhaps, using some kind of internal preview?

Strange, this is what I see: https://imgur.com/a/sgtVt2O

I'm based in the UK, I wonder if that makes any difference