T.K.
I have no idea what the style name is...when I was looking for mattresses for my kids, I walked into a Sealy store and told them I wanted the least expensive mattress and box spring set they had...and I have to tell you, now, 4 years later, they are still the most comfortable mattresses in the house. They are one step up from the mattress set that came with something like a box spring but it was made with cardboard...
The other thing I have done with the bunkie board mattress that we have on the top bunk bed is get a good mattress topper, like the memory foam topper...or more recently we have used a feather bed topper on top of the mattress. Those are 2 options that are a little less pricey if you aren't ready to make the plunge on a new mattress set.
Good luck!
T.