The first letter of your name is your initial. The first thing you say to someone is your initial greeting. Initial is something that occurs first or at the beginning.
If someone asks you to initial a form, they're asking you to sign by writing your initials on it. If your name is Inna Instant, you would write I.I., and you'd probably write it really quick! The first draft of a paper might be called your initial pass at getting your ideas down. If you say that these are your initial ideas, it implies that you will be coming up with more.