It depends on the hotel and, probably, the country. In the UK hotels charge for the room on the basis of single or double occupancy, but sometimes a single occupancy room will be a double room at a reduced rate. I'd guess they wouldn't be too keen on couples turning up to use such a room when it was booked for single occupancy.

I can't help wondering why you booked a single occupancy room if you were going to stay with your SO? It's hard to think of an innocent explanation and I don't see why you'd be entitled to compensation.

However, if the booking company communicated the wrong information to the hotel then you could expect compensation from the booking company.