SharePoint\System account is special account. Sometime it happens that when you login using DOMAIN/<<UserName>> is display as “System Account”. (Following image)
This is because of when application created or extended, during that time which account specify for application pool identity that consider as “SharePoint/System” account.
But if you want to display your username instead of “System Account” following are the solutions for that.
1. Go to Central Administration Site
2. Go to Security –> Configure Service Account
3. Next page you can see that “Credential Management”.
4. Select your application pool.
5. Select different account. (Other than your account). Which ever account you specify over here for that you can see “SharePoint/System” account.
6. If you still want that your application pool identity should be your name then manually set using IIS Manager.
Let me know if you still have any question about it.