Hello MarilynO
The reservation is required from Domodossola, which is the train’s border station.
Brig to Domodossola makes still part of the Swiss rail network, consequently the Swiss Travel Pass is valid to Domodossola.
If you intend travelling to Domodossola only, you are better off taking the RE trains from Brig, instead of the EC, latter which is often fully booked.
Kind regards,
Roland