Presumably you mean you have diverted to your alternate and now wish to file for a departure? If so, just file it as a normal departure to your next destination. I don't think that ATC would be interested in whether your departure point was your alternate from a previous trip.
No, I think the OP is talking about departing from an airport when the weather is below the minima required to make an approach at that same airport and is therefore required to plan a suitable alternate relatively nearby (IIRC within 30mins flying time on one engine, but i may be wrong). This allows for the fact that they won't be able to make an immediate return to the departure point in the case of an emergency. It's more of a concern for the airline's ops department than ATC: if you want to divert (at any stage of your flight) tell me where you want to go and I'll arrange it. At that stage I really don't care what's written on your flight plan.