Hooks are usually named for their shape (eg L, C, S) or their use (curtain, fish, picture). I've shown some common hooks below that might be useful as substitutes for your first two examples.
A good way to be educated on what various bits of hardware are called is to go to a good local hardware store where they have nice displays of these things. Usually there are two displays: one is for specialized hardware for vehicle towing, and the other is for more general construction and project hardware. I learned a lot by studying those displays. It's better than doing it on line because you can pick the things up, play with them, get a feel for what they may or may not be capable of.
Here are a few examples that resemble some of your photos, and may be useful.
S hooks (various combinations of open or closed, long or short, twisted)
Perhaps what you're trying to do in the third picture resembles a D Ring Hook (eg on the back of a picture frame)
D Ring Hook
or perhaps you mean something like this