- What is its exact name so that I may google better for information.
- More specifically, I have a similar one with a damper added on top which is getting slack and mis aligned, possibly because of rust (its right under the sink and frequently gets wet). Is it possible to make it last a little longer and tighten it or adjust it in anyway or would I need to just replace it?
That is a 35mm cup hinge, sometimes known as a Euro hinge.
They wear out over time, so replacement is a cheap and cheerful option. If you buy a cheap one (say, at a big box store), you'll need to replace it at some point; if you buy a Blum/ Hafele/ Salice or other high-end replacement, it'll last as long as the cabinet.
When buying, you'll be faced with a staggering number of options regarding "overlay" and opening angle. Best bet is to remove the existing hinge and bring it into a brick/mortar place. Otherwise, a bit of work googling will allow you to match it up. One other option: you can get ones that clip on (as opposed to being screwed in place), which is very convenient.
Be gentle with the screwdriver when re-attaching the hinges... particle board won't take much abuse. A toothpick and some glue in the hole might help if things feel loose.