This is coming from someone who worked in the hotel industry for well over a decade for almost ten different hotels across multiple states in the US. Everything is coming from my own personal experience working the front desk.
Tell the front desk specifically this: "I would like to be invisible and anonymous. If anyone calls or asks about me, I am not here. I do not want any calls transferred to my room, and please put a Do Not Disturb (DND) on my phone.".
I would bet good money that they will simply say ''Okay'', and make it happen, but if for some reason they ask why you want this, tell them that you are hiding to get away from your abusive ex, and that you would be in serious danger if they found out where you were. That is a very real situation that front desk workers have encountered too often, myself included. That would cause them to treat your instructions very seriously, both out of compassion, and also out of concern for the hotel's own liability by violating customer privacy, far more so when violating that privacy puts the customer in danger.
With this, the front desk will tell anyone that asks about you (except for the police) that they don't have your name on the guest list, and that you are not staying there. The police don't have any kind of network access to the hotel's guest list, so if they did have any reason to look for you in a hurry, and they have reason to believe that you are at a hotel, they would have to call every hotel in town individually. Technically they need a warrant for this, but most hotels simply comply to get a criminal out off their property.
The DND on your phone means that the hotel's switchboard phone system will automatically block any incoming calls to your room and give a busy tone, except for those coming directly from the front desk staff themselves.
*********************
And I wouldn't worry about using a card to check in unless someone that personally knows you has ready access to your card's transaction history, AND they have some reason to check it, AND that seeing a hotel deposit pre-authorization would mean there is some kind of emergency.
Hotels do not give out financial information to anyone including the police. If the police had a warrant, which they wouldn't unless you are a wanted criminal, they would contact your card provider directly.
**********************
Tell the front desk that you don't want housekeeping because you normally sleep during the day, and that you will bring your dirty towels and sheets to the desk and trade them for fresh ones when you are awake. That is a very common thing that hotel staff are used to. Regardless of whether or not you actually intend to trade them out, doing this will prevent your room from ever being put on housekeeping's cleaning list in the first place.
***********************
Create a timed email to be sent to the police a few hours before check out informing of your CTB, and they will take it from there. The hotel will not have to be involved.
***********************
Yes, you can check in business as usual, and it best that you do. Hotel staff aren't detectives or mind readers, and they don't call the cops or give the customer problems at check in unless the customer is being an insufferable jackass (again, speaking from personal experience). Their feet hurt, they make ten bucks an hour, no lunch breaks, and they just want their shift to be over so they can take off that stupid name tag (again, speaking from personal experience).
************************
Sorry that this became a small novel, it's just something I know a lot about from the hotel side of things, and I saw a chance to make things easier for both you and the hotel.
If you have any more questions about this kind of stuff, by all means ask away. :)
************************
Oh, and before you CTB, leave the hotel a good review. They've earned it.
EDIT: Lol thanks for the likes, I think I just became the travel agent....OF DEATH! Helping to shuffle off this mortal coil with a free continental breakfast (some restrictions apply). Don't eat the scrambled eggs.