No really, what is it that you actually do? If 80% of the time, you’re doing (x), then you are an (x) designer. If you come in at early stage and ideate on the user flows, you can call yourself an Interaction designer. If you design early-mid stage wireframes or prototypes, call yourself a Prototype designer. If you design the final interface, call yourself a User Interface(UI) designer. If you design icons, illustrations, you can be known as a Visual designer. Animations? Motion designer.
Companies use the term ‘Product Designer’ differently; the most general definition is a person who’s a champion of a user’s needs. As Justin Edmund said, “A product designer oversees product vision from a high level (how does this feature make sense for where we want to be in 6 months) to a low execution level (how does styling this button this way impact how the user flows through this function).”