You can probably recognize the modes as "major-ish" or "minor-ish". Then you can recognize specific modes by how they differ from the regular "major" and "minor" sounds you're familiar with. For example, Phrygian is like minor-flat-2. You could learn it as the "minor-ish" sound with that flat-2 sound. Since you said you want to recognize the scales played as a scale, simply playing the scales yourself will really help ingrain the sound in your head. Learning to hear it in music is arguably more important- to that end, I'd recommend listening to and playing music in that mode.
You might not need/want emotional labels for the sounds. This is sort of like the old "major is happy, minor is sad" deal. I think this teaching tool works with new musicians because they are already familiar with both sounds (from popular music) and they already have this classification in their head (most of the happy songs are major, most of the sad songs are minor). But, remember that the goal is to learn what major and minor sound like. This heuristic doesn't really identify major and minor- I've seen comments like "This must be major because it sounds happy" on songs that are clearly minor.
You already made a connection for yourself with Dorian, which will help you connect "Dorian" with the sound you've heard ("dreaming minor") but haven't had a label for. But if you don't recognize the sound of the other modes as anything, then there isn't much benefit (for ear training) to attach someone else's emotional label to them.