Mostly a business card is fine.
(Imagine you are on vaccation, why should you have your office badge with you? ) Here in europe mostly it is only a plastic card with a code or a small badge.

I have been asked to provide proof mostly in China. But not always.
Sometimes they asked, sometimes not. Normally they ask only the first time you stay at the hotel. (happened to me at GH Shenzhen, stayed like 4 times there, after the first time they didnt ask anymore for a card)
Others like the GH Guangzhou or Hyatt on the Bund didnt even bother to ask.

As during the trip I was kind of running out of cards: I mostly asked them to make a copy, no problem with that.