The term "assembly-man" is primarily used to refer to a member of a legislative assembly or parliament. However, there are several other synonyms that can be used to describe such a person. These include "lawmaker", "legislator", "congressman", "representative", "politician", "council member", and "delegate". Each of these synonyms represents a slightly different perspective on the function and role of an assembly-man, but they all ultimately refer to someone who is responsible for representing the interests of a particular constituency and helping to shape policy and laws that affect their constituents.