When we use the phrase "made off the top one's head," we mean that we are speaking or improvising without any prior knowledge or preparation on the topic. Although this phrase is commonly used, there are several synonyms that we can use to express the same meaning. Some of these synonyms include "spontaneously," "impromptu," "unrehearsed," "extemporaneous," and "off the cuff." These synonyms give us variety when expressing the same idea. Whether it's a speech, a conversation, or an improvised performance, using these synonyms can add some color and flair to our language.