Hose Replacement
 

I am not sure what hose this is on my Cherokee XJ, but I need to replace it. What hose is this called and the thing you attach it to?
https://cimg8.ibsrv.net/gimg/www.che...a7407bf50.jpeg
https://cimg2.ibsrv.net/gimg/www.che...50a5c98e8.jpeg

Those are sometimes hard to find new in the size you need , I get them a the junk yard off other cars most will have them so you can find some good ones .

what is the hose called?

I believe that hose is part of the evaporative purge system and probably goes to the canister purge pump or the carbon canister itself. Right now, it's a vacuum leak!

Your shot is not the best but here goes nothing.
So I am guessing you have 3 nipples on the side of the intake manifold.
What year is your Jeep and is it Federal Emissions or CA Emissions?
Is there a check valve looking thing on that hard plastic line you are holding in your hand?
If so does it look something like this?

https://shop.advanceautoparts.com/p/...E&gclsrc=aw.ds

If not and it is just hard plastic line I am guessing that it goes in the nipple on the side of the intake manifold closest to the radiator.
And if that is true just go to the auto parts store, get a short length of hose (3" maybe) that fits somewhat securely on the plastic line and attach it to that nipple.
Usually there is a an elbow there. Which might or might not be the one in your hand.
I really need to see a shot of that area just a little wider, and clearer, to make out what you are missing.

Hose Replacement
 

Where does the other end of the hose go?