My mystake was to assume that sys.fn_cdc_get_min_lsn()
accepts the table name. I was mostly misguided by the examples in MSDN documentation, probably and didn't check the exact meaning of the parameters.
It turns out that the sys.fn_cdc_get_min_lsn()
accepts the capture instance name, not table name!
A cursory glance at my current capture instances:
SELECT capture_instance FROM cdc.change_tables
returns the correct parameter name:
ordering_Fields
So, one should use underscore as schema separator, and not the dot notation as it is common in SQL Server.