How to add claims in a mock ClaimsPrincipal

You don’t need to mock ClaimsPrincipal it has no outside dependencies and you can created it un-mocked:

var claims = new List<Claim>() 
{ 
    new Claim(ClaimTypes.Name, "username"),
    new Claim(ClaimTypes.NameIdentifier, "userId"),
    new Claim("name", "John Doe"),
};
var identity = new ClaimsIdentity(claims, "TestAuthType");
var claimsPrincipal = new ClaimsPrincipal(identity);

And I’m not sure what you are testing here. Certainly “John Doe” will not be part of viewResult.Content because it is never been set to this.