Hey there house2fly!
So the way the adventures are set up is just like before; there's minor, average, major, etc. The generic adventures have all been replaced with named adventures, but it's still broken up into the same tier system.
This means if you end up doing all of the "major" adventures with names, you'll start to get generic "major adventures" when you roll for one of that tier. So it's very possible to end up getting generic adventures in between named adventures, provided your stronghold stays around the same prestige level and you are consistently given the same tier of adventure.
Hope that clears things up, and thanks for the input!