Guten Tag, BraunL.
Although, in der Schweiz, you are quite likely also to hear "grüetzi," grüessech (Bernese) , or sometimes the Bavarian "grüss Gott."
<<"Two seats side by side seems better, but if common practice is not to reserve a seat, then we may just wait and try our luck .
We are travelling on a Monday, late morning, so I would think it will be less busy.">>.
I have been visiting Switzerland since 1980, and have only reserved on trips to or from Italy (Milano), Austria (Vienna) and Hannover.
Not even to Strassbourg, when we (a party of three) went from Zürich to the have lunch at the Orangerie.
Over those 37 years, the rush hour trains to/from the main cities have become more crowded, so that if I go from Bern to Burgdorf at 1700 or 1730 these days, I buy a First Class ticket, for modest extra cost, and that almost guarantees a seat, even when the second class cars are quite full.
In between rush hours, including the time that you are traveling, there have always been seats available for two people together in 2nd class.
I am not sure which route you have chosen, but the most likely one will take you to Bern, then Spiez, and then through the new "Lötschberg Basis Tunnel" to Visp in the Rhonetal. From Visp, change to the meter gauge line to Zermatt.
A significantly more scenic route than the "Lötschberg Basis Tunnel" is to take the upper route, on the old rail lines via Kandersteg. It takes about an hour longer. It makes a lot of local stops.
That option uses an hourly train called the Lötschberger from Bern to Brig ( quite close to Visp). The narrow gauge line for Zermatt is available at Brig platform 14, (across the Bahnhofplatz) so pick up the line to Zermatt in Brig and go onward through Visp. The Lötschberger has large windows and nice rolling stock. In this case, it the name refers to the higher, old route through the Lötschberg Pass, with a short tunnel section from Kandersteg that emerges at Goppenstein, and goes down the south facing wall of the Rhonetal to Brig.