Whenever I've had experience of a departure alternate being nominated, it was by way of a radio call to the tower prior to departure. The info was passed onto the next (departures/approach) controller by phone.
I don't think there's a formal place in the FPL for it. You could enter it in the remarks section, I guess. But it's just as satisfactory to let the tower know before departure.
If nobody knows, it's no big deal, either, IMO. If you have an 'event' requiring the use of a departure alternate during or immediately after takeoff, it's likely to be an emergency, and the ATC unit handling you will quickly ascertain what you want to do and where you want to go.
ATC generally doesn't have a plan, or "sanitize" airspace based on a nominated departure alternate. We just make a plan as required, if it happens. I guess that's why there's no formal space in the FPL for it.