So I am developing a game and trying to find one of those to use, but I don't know what to search for. If you don't know what I am taking about, look at these examples:
What are these called?
"Crosshairs" or an "aiming reticle," usually. Probably also "aiming dot" and similar variations.
In addition to what Josh Petrie mentioned: if you're looking for more advanced ways to aim weapons, the center dot in your bottom image is also called a "pipper" in real-life applications.
This especially applies when some device is actively predicting where an arcing projectile will impact, like a bomb or grenade, instead of simply showing which direction it will go when fired/thrown/dropped.
Aircraft HUDs combine pippers and reticles to convey extra information about complicated firing solutions, as shown in this example:
So in your third image, the circular arcs are the reticle, while the center dot is the pipper.