How do I specify different Layouts in the ASP.NET Core MVC

You can still do something very similar to your original approach, using ViewData to pass around the layout name (Although I would create it as a Result Filter):

public class ViewLayoutAttribute : ResultFilterAttribute
{
    private string layout;
    public ViewLayoutAttribute(string layout)
    {
        this.layout = layout;
    }

    public override void OnResultExecuting(ResultExecutingContext context)
    {
        var viewResult = context.Result as ViewResult;
        if (viewResult != null)
        {
            viewResult.ViewData["Layout"] = this.layout;
        }
    }        
}

Then in the _ViewStart.cshtml file:

@{
    Layout = (string)ViewData["Layout"] ?? "_Layout";
}

Finally, assuming you create a new layout like Views/Shared/_CleanLayout.cshtml, you can use that attribute on any controller or action:

[ViewLayout("_CleanLayout")]
public IActionResult About()
{
    //...
}