For example, I’d like to have a color called “text-color” or one called “content-box-color”. How can I save a color like this and then assign it to an element?
Check out the wiki on Inkscape swatches.
Also if this isn’t what you’re after, there is a free program called Colorpic which is a standalone program that can pick up a color from anywhere on your screen and save it in a labeled palette 🙂
I use it every day.