I think something like this came up before a few months ago but for something else.
There was an answer where we decided that one possible configuration could be to put a unique ID into the @anvil.server.callable like @anvil.server.callable("origional_func_name" + machine_id) when the script is run from a specific place, registering the name of the function apended with a unique machine identifiable ID once the script is run and connects to anvil, registering the name.
The unique ID’s do not have to be hard coded, they could be gathered at run-time from the system that runs the script (like a salted, hashed UUID or something), and stored in an anvil data-table and retrieved to a variable that would be passed to anvil.server.call().
In this way you could know exactly what machine was running what function, using identifiable information.