If you pay a housekeeping service or you pay a person who advertised as a housekeeper but who also does a lot of other clients, then you are hiring a small business person. You don't issue them any tax forms such as a 1099-MISC unless you are a small business yourself and your business has hired this person. They are a small business/independent contractor and are responsible for their own taxes. Your expenses for cleaning are not deductible if they are personal expenses, they may be deductible business expenses.
If you determined that this person is your household employee, then you need to issue them a W-2. The amount you pay is not deductible on your taxes and more than it would be deductible if you hired a cleaning company.
Start here for more info https://www.irs.gov/taxtopics/tc756.html