The phrase "does off top your head" is commonly used to ask someone if they can think of something quickly, without taking time to research or think deeply. Synonyms for this phrase include "off the cuff," "offhand," "on the fly," "impromptu," and "spontaneous." These words all convey the idea of something done or said without much preparation, or without the benefit of deeper thought or analysis. Whether you're looking for a synonym to use in casual conversation or in a more formal setting, there are many options that can help convey your meaning and convey your message quickly and accurately.