It sounds as though the property may not have been sold yet. Yes, normally the deed would already show the lender’s name if they currently own the property. If you have already brought this to their attention and they have not responded or done anything I would recommend you find out about free legal services in your area. Sometimes there are open forums from Legal Aide groups wherein you can ask your question of an attorney.
The deed is not changed until the lender takes complete ownership of the home which does not occur just because you have moved out. You are still the legal owner of the property.
If you want to walk away, you could initiate the process to deed the property to the bank. This is called a Deed in Lieu of Foreclosure.
Another option is to move back into the home. You will only have to pay the utilities and wait until they get around to evict you. Obviously they are not in a hurry to reclaim the property so you could live there rent free for months if not years.
Since you are still the legal owner, you can rent out the property. Even if the bank finally gets around to foreclosing, the tenant can stay in the property (if there is a lease agreement) and pay the rent to the bank.