Passing objects into functions

This is how the hooks work: when WordPress gets to a line where it executes code attached to a particular hook, WordPress itself passes in the correct object for that context. You would then need to look at the Codex or any other WordPress reference to know what that particular object contains.

In terms of what you would name the object in the argument of your function, it makes no difference; it merely represents or refers to the object being passed into the hook, it's not meant to be the actual name of the object.

I would suggest reviewing how PHP functions work, particularly with arguments. When a function is declared, the argument is a variable declaration that's initialized for the function scope (it more or less exists only in the function itself). It's a weird concept to wrap your head around (it took me a while, trust me), but once you form a correct mental concept, it becomes much clearer.

So, you could use the same variable every time, e.g. $my_wp_object, but it's usually better to stick to something that makes sense for that particular hook. The examples given in the Codex are a great starting place.