Do hotels offer "proof of stay" certificates to their guests?

I'm not sure what to call the document that I'm referring to, so I used the term "proof of stay."

I'm scheduled to travel to Latin America with a colleague of mine to attend a work-related conference. We're sponsored by our company, but our company is a research facility that receives grant money from the government. The government apparently requires us to provide "a document proving that X and Y stayed at the hotel for the duration of the conference with each of their names stated on it."

I've personally never heard of this before. I've contacted the hotel we're scheduled to stay at, and all they keep saying is that "yes, you can request an invoice when you leave." However, it's not exactly an invoice or billing statement we're looking for.

I'm just curious if anyone's heard of documents like these, and what we should be calling them or requesting on behalf of the hotel? I feel like many people traveling on their institution's dime may have faced this kind of situation and perhaps my unfamiliarity is also causing confusion.

Thanks.