When it comes to finding synonyms for the phrase "puts down for," there are several options to choose from. Some alternative phrases include "assigns to," "designates for," "nominates for," or "appoints to." Each of these phrases suggests a sense of purpose or intentionality, suggesting that the subject is putting someone or something into a specific role or position. Other possible synonyms include "selects for," "chooses for," or "names for," all of which carry similar connotations of choice and decision-making. Ultimately, the right synonym will depend on the particular context and the intended meaning behind the phrase.