The term "distance function" is commonly used in mathematics and computer science to measure the distance between two points in a given space. However, there are several other synonyms for this term that can be used depending on the context. For instance, "metric" is a common synonym for distance function and is used to measure the distance between points in a mathematical space. "Cost function" is also a synonym for distance function in the context of optimization and machine learning. In addition, "similarity measure" is a synonym for distance function that focuses on measuring the similarities between two objects. Overall, these synonyms provide alternative ways to describe the concept of measuring distances between points in various contexts.