There are several synonyms that could be used for the phrase "make up off the top of head". Some possible options are: improvise, ad-lib, extemporize, wing it, brainstorm, and freestyle. These words all convey the idea of creating something on the spot, using one's creativity and resourcefulness to come up with a solution or idea. Whether it is coming up with a story, speech, or solution to a problem, the ability to think quickly and make up something off the top of your head is a valuable skill that can be useful in a variety of situations.