When you're composing a message, the "From:" field has a pull-down menu that shows your primary address and your extra mail address. Click and hold down "From:" to select your extra mail address, if you want to use it.
Recipients will see that address.
If you want, you can make your "extra" address the default address in the "From:" field. That way you don't have to choose it, it's just there, every time. Making it your default address is also easy. Here's how:
Now you don't have to select this address from the pull-down menu anymore. It's selected already!