Given out is a commonly used phrase that refers to the distribution of something. However, there are other phrases and synonyms that can be used instead of given out. For example, "handed out" is a synonym that means to distribute something by giving it directly to someone. "Issued" is another synonym that means to distribute something formally or officially. "Dispersed" is also a synonym that means to spread out or distribute something widely. Other synonyms for given out include "distributed," "allocated," "divided," "assigned," and "apportioned." By using these synonyms, you can add variety to your language and make your writing sound more interesting and varied.