I've had consecutive booking in three different hotels over the last two years.

Mercure, Sydney, Australia
No issues. Everything was perfect. Additional welcome drink vouchers were slipped under our door on the first day of the second booking.
One invoice issued at the end of the stay.

Mercure, Bratislava, Slovakia
A few days before the stay, I received an email from the hotel saying they could see two consecutive reservations and confirming I wouldn't have to change rooms and I'd get one invoice.
At the hotel, the receptionist only checked us in for the first booking and couldn't understand why I protested. I guess she was a new employee and spoke very poor English. A more experienced receptionist took over. We were upgraded to an executive room for the whole stay. One invoice was issued.

Mercure, Florence, Italy
The reception didn't notice we had another reservation until we pointed it out on the last night of the first stay. It turned out the company had made a mistake and reserved a different room category. The receptionist insisted on us paying the difference (15 EUR for the last night). We declined as we didn't want to spend any money at the hotel after a rather frustrating stay at the hotel. In the end, we had to move to a standard room, which turned out to be smaller than superior rooms, but at the same time was more functional and cosy. It also offered a better view and more privacy.
We had to do a full check in (passports were scanned again; credit card verified etc.), as -- according to the receptionist -- their system only stores this information for 24h after check-in.