If you are using the template ASP.NET MVC with Identity, by default it already saves the Username with the email provided in the method Register, look at you:
[AllowAnonymous]
[ValidateAntiForgeryToken]
public async Task<ActionResult> Register(RegisterViewModel model)
{
    if (ModelState.IsValid)
    {
        var user = new ApplicationUser { UserName = model.Email, Email = model.Email };
        var result = await UserManager.CreateAsync(user, model.Password);
        if (result.Succeeded)
        {
            await SignInManager.SignInAsync(user, isPersistent:false, rememberBrowser:false);
            return RedirectToAction("Index", "Home");
        }
            AddErrors(result);
    }
        return View(model);
}
You can modify this behavior... like?
Change your class RegisterViewModel:
public class RegisterViewModel
{
    [Required]
    [EmailAddress]
    [Display(Name = "Email")]
    public string Email { get; set; }
    [Required,Display(Name = "Username")]
    public string Username { get; set; }
    [Required]
    [StringLength(100, ErrorMessage = "The {0} must be at least {2} characters long.", MinimumLength = 6)]
    [DataType(DataType.Password)]
    [Display(Name = "Password")]
    public string Password { get; set; }
    [DataType(DataType.Password)]
    [Display(Name = "Confirm password")]
    [Compare("Password", ErrorMessage = "The password and confirmation password do not match.")]
    public string ConfirmPassword { get; set; }  
}
And in the View Register.cshtml add the field that will receive the Username
<div class="form-group">
        @Html.LabelFor(m => m.Username, new { @class = "col-md-2 control-label" })
        <div class="col-md-10">
            @Html.TextBoxFor(m => m.Username, new { @class = "form-control" })
        </div>
    </div>
Once done, change what the Username is receiving in the method Register in AccountController
var user = new ApplicationUser { UserName = model.Username, Email = model.Email };
And ready, your Username will have the value informed at the time of Registration. =)
							
							
						 
Some answers to OS questions indicate using
User.Identity.Name; has tested?– rLinhares
Thus the error indicating that there is no argument provided that corresponds to the required parameter.
– WPfan
Using Windows Authentication? Or what form of user authentication?
– Felipe Grossi