There are several possible synonyms for the phrase "hamburger patty frying machine," depending on the context and the specific type of machine involved. One possibility is a "burger grill," which typically uses heated plates or grates to cook multiple patties at once. Another option might be a "patty maker" or "patty press," which forms and shapes the ground meat into uniform discs before frying. Alternatively, a "flat top grill" or "griddle" could refer to a larger cooking surface that can handle multiple items, including hamburger patties. Other variations might include "burger fryer," "hamburger cooker," or simply a "fast food grill".