Your online identity is how you present yourself on the Internet. In the real world, the law generally encourages us to use our real names.
I, for instance, am Allison Figus in the real world. Right now, I'm also Allison Figus online. That is a valid way to use your online identity.
You could also use a screenname. You could make up a semi-unique identifier such as carrottop and use that online instead of your real name.
What is not valid is pretending to be some other real person on the internet. That is Cat-Phishing. It's not very cool. It just hurts a lot of people.
Websites that let you make an account will generally have you create a unique online identity. You'll be asked to come up with an identifier, but it won't always be called that. Most commonly, I see websites calling this your username. Sometimes, you'll be forced to use your email address as the identifier. Other times, it will just be an option.
2. Theory: The Uniqueness of Identity
Your username must be unique to a given website.
Website domain names are unique.
The combination of domain-name:username is a unique identity for you on the web.
I see you wily students out there raising your hands already:
What if a domain hosts multiple web apps?
Well, that is a good point. Some domains do that. It's a PITA to administrate on the back end. When I've worked on systems like that, we generally had a Common Identity Store.
So, in good practice, even when a domain hosts multiple web apps, each user will only have a single identity across all apps on the domain.
3. Identity Management Systems
If you want to sound formal when you talk about how you store your usernames and passwords, call it an Identity Management System.
Identity Management Systems can be quite informal or quite sophisticated.
3.1 The Minimalist Approach
The bare minimum for an Identity Management System should be a well-designed database:
Strong Passwords for Administrators
Unique Administrator Identities for each Administrator
A Well-Salted Password Field
3.2 The Powerful Pre-Packaged Approach
Sometimes, you want to go complex but you want it to be simple. There are always great pre-packaged solutions out there.