I don't know if there's an official name to them but can anyone recommend some short series (the ones that are usually like 10-15 minutes per episode). I've recently been into them but since a lot of them have low ratings it's hard to tell which ones are good.

I can't recommend Nightmare Teacher enough. The production value is rather low, but the acting is on point. I personally like its theme and storytelling, even though the short running time and small episode count mean that some things are left unexplained.
Splash Splash Love is short. I has 2 episodes (1hr each). 
+1 Splash Splash love
Baek Hee Has Returned, 3 episodes had me in hysterics, 1 episode made me cry my eyes out.  this drama does more in four episodes than most do with 16.  it's silly, dark, romantic, embarrassing, fun, hilarious and moving
Naked Fireman
+1   to Back Hee Has Returned. I agree to Naksken about how good this short series is. 

Another suggestion is Noble,Noble my Love with 20 episodes x 15mins each. 
High end crush 
+1 Thumping Spike

See also:
- DramaWorld
- Love for a Thousand More
- Spark
Splash splash love and DramaWorld are one of the bests...

Page Turner
Star of the Universe
109 Strange Things
The Best Future
Positive Physique
Vampire Flower
Love Cells
Click Your Heart
Muhan Company
+1 splash splash love (very cute & funny)
+1 nightmare teacher 
+1 page turner (i love both actor so much, and the story is great too)

the day after we broke up (the ending is a bit weird in the sense that the viewer seems to have missed some info/scenes before a time jump), but it's really good & very cute story