Klaviyo being a non-relational database means it doesn’t matter what you call it. Klaviyo doesn’t care, there is no “column” for this event and there is no right answer. Call it whatever you want.
99% of Klaviyo’s documentation and the use of “Active On Site” metric has to do with Klaviyo’s integration with Shopify. So “active on site” becomes sort of a colloquial default if you will. Since you are doing a custom integration you can call it whatever you want. Using Active on Site may make some of the reports auto populate, but you can make reports for whatever event name you want to.
Whatever you choose be sure you are CONSISTENT in your event name.