A Russian-based company issuing tourist visa invitation does not seem to care about me having a hotel booking, nor do they say it will go on a visa. They only ask for a hotel name, and claim that this is just for formality. Upon attempting to entry Russia - do the border staff ask for exact address place of stay in Russia, and does it necessarily have to be a hotel, or can it be a private home (despite the fact that one is travelling on a tourist visa)?
I believe the answer is no.
I made a booking on the Trans-Siberian in 2006. The booking agency arranged the documentation for my visa which I took to the relevant office (in London) for my visa application. The visa was issued. My "accommodation" in Russia was listed as the train itself. I did not have my tickets for the train because I was due to pick them up in Moscow, three days after I arrived in Russia (I spent 3 days in St Petersburg first).
I kept copies of that paperwork for when I entered Russia by train from Finland but they did not ask me for it.
I have been told this "hotel booking" requirement is simply a formality from the old USSR days.
As far as I know, on crossing the Russian border you do not need to tell the exact address where you will be staying.
Before crossing the border, you should fill in a migration card - there will be a field for the name of agency which issued an invitation.
After arriving in Russia you have 7 days to register you place of living. If you stay in a hotel, hotel staff should prepare documents for you. If you stay with a friend - ask him to register you. If you stay less than 7 days in one place you don't need to register.
Migration cards look like this:
When I went to Moscow on January 2015, the staff who were extremely angry-looking females asked me with a really bad English that what the purpose of my stay, how long I will stay and If I have a confirmed booking on a hotel but did not want any paper of proof for hotel confirmation or even travel insurance papers.
So it was easy to pass that exam :)
I crossed from Estonia in 2012, and only showed my visa. My sponser was a travel agency, and I never booked a hotel (couchsurfed). Nobody ever asked where I was staying and I didn't have any problems.
You don't need to provide any proof of your hotel booking. If someone ask you for address, just tell them the address you have written in your tourist voucher. Same address you need to fill into your migration card.
In case you don't have address in your voucher (Usually it's there): If you going for less then 7 days then you can tell and write your real place of stay, any.
If you going to stay longer then 7 days then tell address, where you going to be registered. (Hotel, host etc.)