Zentralbahn (subsidiary of SBB) operates that route yes. "Golden Pass" is a marketing name, nowadays mostly used for Interlaken - Montreux.

What do you want to do exactly?

Seat reservations are not a thing in Switzerland: simply hop on and sit wherever you want. There is enough seats.

If you want to look at timetables use SBB app. It's very reliable and covers the whole country (or actually most of Europe).

There are hourly trains between Interlaken and Lucerne, all stopping in Brienz (+ a few extra services on weekends and in summer).

Thank you. I want to take the Golden Pass Line. So I’m just confusing which one is the correct one? Luzern-Interlaken Express? 

Well I don't know... As I said the Golden Pass marketing name now relates to Montreux - Interlaken (with the gauge changing in Zweisimmen).

But every bit is scenic : Montreux, Interlaken, Brienz, Lucerne and even all the way to St. Gallen.

The route between Interlaken and Montreux is sometimes called the Golden Pass Line. Sometimes the whole route from Luzern via Brünnig to Interlaken and then on to Montreux is called the Golden Pass Line. The most beautiful part of the route is the part from Interlaken to Montreux. Sit on the left hand side of the train when leaving Spiez for the most beautiful views. The route from Interlaken to Luxern does not have equally beautiful views as you are travelling away from the Alps.

You don’t need to travel with a specific train.

Oh Thank you. To be honest I’m now a bit disappointed about my plan haha. But I believe I can still have great views on my way to Luzern. 

Don't worry, it's still pretty scenic. You can't go wrong with Swiss railways!

For the best views try to sit on the right when boarding -> lakeside.

The train reverses in Meiringen and you'll get great views all along.

Side note : boats on Lake Thun and Brienz are fully included in Interrail. It's a fun experience! :)