OS X is an account-based system, in which individual users have their own accounts storing their own settings and data. When you set up a user account, the system will ask you for your name and then based on that will create a short username the system will use to identify your user account.
This short username is the true username of the account, but you can use the short name or your full name at the log-in window. Since the system initially generates it for you, it's easy to overlook the fact that you have the chance to choose a different log-in name.
For example, if you type "John Smith" as your name then you will be given "johnsmith" as your username. However, if instead you would prefer to use "jsmith," "js," or another name altogether for logging on, then you can set up an account alias that lets you do so.
To set up an alias, go to the Users & Groups system preferences and authenticate as admin by clicking the lock. Then right-click your account and choose the Advanced options, where you will see fields for editing the username, user ID, and other details about your account. Leave the "Account Name" field intact, and click the plus button to add an alias to the account (if you use iCloud and other online services then you may see some aliases already used).
On clicking the plus button you will see a new line appear with "New Alias" in it, so edit this to be the name you would like to use for logging in, and save the results. After doing this, log out to get to the OS X Login window, and use your new alias to log back into your account. You can create multiple log-in aliases.