If it's on a public desk (someplace where employees are interacting with customers) and on the customer's side of the desk, I assume it's for customers to use. If it's on the employee's side of the desk, it's for the employee.
In someone's office space, I would ask, even if it's on my side of the desk.
I know the distinction I'm making, but I'm not sure it's clear. I'm a librarian, working the reference desk. There is a bottle of sanitizer, provided by the library, on the desk, usually on the patron's side (though they do migrate). It's next to the little pencils for them to use. Some people do ask, but it's not a problem if they don't (in fact, if they kept asking, it would be annoying to keep answering the question.)
In the back office area, where patrons aren't supposed to go, I have my own desk. I have my own personal supplies there, including a good hand lotion and Kleenex (not the cheap tissues provided by the library). If someone, for some reason, were at my desk, I would expect them to ask if they can use my personal supplies.