Some synonyms or related expressions for "two-year anniversary" could be:
Bicentennial: This term is more commonly used to refer to a 200-year anniversary, but in a more general sense, it can imply a significant anniversary period. However, it is not as specific as "two-year anniversary" and is usually reserved for much larger time spans in historical or national contexts. For example, a country might celebrate its bicentennial of independence. It has a more grand and momentous feel compared to the relatively short two-year mark.
Second anniversary: This is a straightforward and commonly used synonym. It clearly indicates the second year of an event or relationship being commemorated. For instance, a couple might celebrate their second anniversary of marriage. It is simple and easy to understand, just like "two-year anniversary", and is used in a wide variety of personal and professional contexts where the passage of two years since a particular starting point is being noted.
Biennial anniversary: "Biennial" means occurring every two years. So, a biennial anniversary specifically emphasizes the two-year cycle. It can be used in the context of an event that happens regularly every two years and is being commemorated on that cycle. For example, a biennial art exhibition might have its biennial anniversary celebration to mark the second iteration of the event two years after the first one. This term is a bit more formal and technical compared to "two-year anniversary" and is more focused on the recurrence aspect.