Even though I suggested Pocket Dimension, I actually like Pink Dimension the best.
Rose's Dimension is not accurate imo. Aren't we changing the name because it's inaccurate now? Before it was Lion's Dimension but now it also connects to Lars. Maybe before it was Rose's Dimension because she brought Lion back to life, but now it also connects to Lars and Steven brought Lars back to life. It's just as much Lion's as it is Lars'. It's just as much Steven's as it is Rose's.
And yeah it can also be used as a pocket to store things. But it seems like now it's not going to be used just for storage anymore. If you can enter one end and exit the other, it's more like a tunnel or a transporation method. So it has more than one use now.
Pink Dimension just seems the simplest and most accurate. Just my opinion tho.