I've tried to search for the name of the connecting mechanisms on these clips but I can't find it. I'm trying to build something where two parts are connected on one axis (diameter less than 5 mm) but each moves independently. So I need a connecting mechanism which doesn't let them come apart but which is also small enough to fit in that hole. What are some mechanisms that would allow this?
IMHO, they are both variations of the pin joint or [revolute joints] (https://en.wikipedia.org/wiki/Revolute_joint) or pivot joints.
Regarding how you stop the pin to fall out over time there are many ways. Interference fit or other types of frictional connections are not an option if you are after a freely rotating joint. Usually you will implement one of the following (not exhaustive)
- some type of safety pin or split pin
- using rivets