Doors – What’s a hinge called for a two-door corner cabinet

Remove the screw and hinge. Break apart a wooden toothpick and place a few pieces in the existing hole. For extra help, you can combine the pieces of toothpick with a little wood glue. This will help hold them in place before the door is back on and also add extra stability once dry. Then put the door back on and use the existing screw. This should help hold it in place for a while.

In my experience, this will last a few years, and then when it gets loose again, do it again. It will be like new.

Take pictures and measurements. (Measure EVERYTHING on the hinge - height/diameter of pin in particular.)

You should be able to find the identical hinge with a bit of effort. Replace the part attached to the wood, and you should be able to drop the welded portion into it. Yes, you'll have to throw out the upper part of the new hinge, but it's the easiest fix and will restore the gate.