It depends on train type and country. E.g. czech operator https://www.cd.cz/en/spojeni-a-jizdenka/ does show this for many trains when having a look at the trains full itinerary. For Germany, the DB Navigator app does show this that way.

I do see IC 793 as an inner austrian train from Klagenfurt to Salzburg, but not into Slovenia? It's a train operated by ÖBB (Österreichische Bundesbahnen).

I do see RE 79036 as a regional train from Salzburg to München. That one is operated by Bayerische Regiobahn. 

Thanks so much, Hector. This is really useful.  I did in the end go on IC 793 - but wasn’t sure who was operating it! (the same train goes all the way from Vienna to Ljubjlana….).  How did you discover that it was operated by OBB?  I have the OBB app but couldn’t work it out.

Salzburg to Munchen - RE 79036 - that proved a bit problematic. It was extremely crowded from Salzburg to Freilassing then (once we had crossed the border into Germany) more carriages were added and the situation eased. Someone told  me that only recently has a RE train done this route - a ‘better’ train did so previously - perhaps due to the recent German rail strikes rolling stock is under pressure?

IC 793 does no such thing, it's Klagenfurt-Salzburg. The direct Vienna-Ljubljana would be EC 151.

bahn.com shows the operators of a train. For international trains, there may be more than 1.

https://www.cd.cz/en/vlak/ - you may enter the train number and scroll down to see the operator.

On this route, you'd have of choice of a few carriers.