depends on the price.. new modern ones are sometimes called tea carts. Moreoften they are fitted to hold stem wear(it hangs under main tray) and wine bottles (on the undershelf), and have a small basket at one end for cork screws and are called wine bars.

expensive antique ones are still called tea trolleys

folding ones (2 shelved, casters, and small handrail) and sometimes just called serving carts.