Assuming you’re using basic letters and underscores, it wouldn’t really take up much more memory. ASCII characters should only take up 8 bits (1 byte). When your code gets run, the compiler won’t really care about the name of your variables. Instead it will work with memory addresses and references.
In their precompiled states a script with longer variable names will consume more memory than a script with shorter variable names. The difference would be negligible though.
Adding onto the good answers, it’s important to remember that some space is always used to store the type of a value (size of a long long as far as I know, usually 8 bytes).
About naming conventions, I use snake case for table keys and functions. I shorten identifiers when they are understandable to me.
Just realized you were talking about identifiers and not values, so the first paragraph is irrelevant.