just take the electronic keycard with you (or leave it in the room) and leave. As long as the room is paid for, they don't care.

I stay in hotels about 3-4 days out of every week and I very rarely actually check out.

I would be careful in giving the hotel your real address however, I am assuming you are married and receiving a survey regarding your stay might be difficult to explain.

Do be careful about the address you give them...  this applies not only local but also out of town.  
 
Don't leave a provider in possesion of a room in your name.  She could convert your out call into an in call...  tied to your name.  The minibar could be used or the room damaged after you leave...  

I suggest you get the lady to rent the room...  and reimburse her the cost.  She might want to actually see your face before doing so...  I waited in the car on one such occasion.  

No, if the room is paid for, just leave the key in the room.  (Note:  make sure nothing incriminating is left in the waste basket!)  
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If you want to checkout yourself (necessary if you want pay by cash) on your way out, tell the front desk you received an emergency call and have to leave early.

..and leave the room whenever you want.   The hotel generally does not care whether there is someone in the room that night or not, as long as they get the money, and you do not bother anybody.

I have not officially "checked out" of a hotel in a couple of years.   They will typically slip your bill under the door, but the maid will throw that away if it is found when cleaning.

Do not worry about that part.

OTOH, though..   Worry about your real name and address being associated with renting a room.  Some hotels might actually call, or send the bill via snail-mail if you do not pick it up.   How do you explain that one to someone else??