Is there a polite way to refer to someone who is responsible for cleaning at work?
Some people might find it subtly insulting if you call them "custodians" or "facilitators", or whatever, when they are really cleaners, as if their true job were shameful. If you clean, you're a cleaner, and there is nothing embarrassing about it that needs to be concealed. Further, euphemisms and needlessly using big words is considered ugly by almost all style books. So just call him a cleaner.
If I wanted a cleaning job and saw an advertisement for a "Facilities Generalist" or a "Habitat Contaminant Removal Executive" I would pass the advert by because I would have no idea what it meant. The last one in particular I would imagine required specialist technical training.
Advertise for a cleaner.
If you have a particular individual in mind who is already in post, I suggest you ask that person what job title they prefer. Some people will want a fancy title, others will be happy with something simple.
"Housekeeping" is the general position name at the hospital I used to work for.
Housekeeping — Business Dictionary
General care, cleanliness, orderliness, and maintenance of business or property. Good housekeeping is an important consideration in underwriting of fire hazard and other forms of insurance, as well as in certification by fire, health, and industrial safety agencies.
"You should have a good housekeeping staff in your office so that it has a good professional feel to it."
"The housekeeping showed up very early and I told them to go away and come back in an hour or two, when I was gone."
How about office cleaner?
Instead of cleaning lady, cleaning woman, consider using housecleaner, office cleaner, housekeeper
The Office Cleaner is responsible for maintaining the overall cleanliness of the facility.
Another possibility not mentioned is concierge. While usually not associated with cleaning duties, in France where the word originated the concierge was (and in some cases still is) responsible for the janitorial duties in many small hotels. As mentioned in other posts it is not the sole responsibility but included among others.