According to a Google search, the word origin is used as the opposite of destination on several pages on the Amtrak web site. Amtrak is the largest train operator in the United States.
Here are a few examples:
This schedule lists the Origin and "Destination" of various routes.
The Interactive Route Atlas page says the following:
Once you have selected origin and destination stations by one of the methods above, click on the 'Go' button to send your custom route request.
The Multi-Ride Ten-Ride Ticket page says the following:
Ten-ride tickets are valid for ten rides within a 45-day, 60-day or 180-day period depending on your origin and destination cities.