Here's the easiest, simplest, and most correct way to handle this. You can not depreciate that which you do not own. Your mother (not you) needs to report this rental and all associated income/expenses on her own tax return. What she does with the rental income (such as give it to you) is up to her.
Your mother, as owner of the house, needs to seek the services of an estate/tax planner yesterday, if not sooner. Otherwise, somebody (probably your mom) is risking a very high possibility of financial rape on the tax front, at some point in the future here. The potential to be taxed into poverty makes the cost of professional help seem like a pittance in comparison. So please, encourage your mom to seek professional help on dealing with her assets that she owns, post divorce. This can be particularly important if your parents were in a community property state at the time of their divorce.
When your mother reports this on her own tax return, take note that "ON PAPER" it is common for long term residential rental real estate to show a loss every single year. So the chances of your mother actually paying any income tax on the rental income is slim to none. And again, what she does with that rental income (such as give it to you) is up to her.
If she chooses to give it to you, then it's a gift. A gift of less than $16,000 in any one tax year is not reported anywhere on any tax return. If it's more than $16,000 for 20222, then your mother (not you) is required to report the gift to the IRS on IRS Form 709- Gift Tax Return. She will not pay any taxes on the gift provided it's less than $11.2 million dollars (and we know it will be less than that.). But the reporting requirement still has to be met if the gift exceeds more than $16K for tax year 2022. (It rises to $17K for 2023).
Take note also that when renting property to a family member/relative, there are things that will raise eyebrows with the IRS. If your mother is divorced from your father (the renter) then this will most likely not come into play.
But overall, nobody should take any action (including what I've mentioned above) until your mother has conversed with a professional. At this point, there's plenty of time. But don't wait until the last minute, as doing so could be costly.
