I think the best approach here is to use class File, FileInfo, DirectoryInfo, TextReader and StreamReaderfrom System.IO especially that you are working on web application.
//Find Directory of the file
DirectoryInfo dir = new DirectoryInfo(Server.MapPath("") + @"\YourFolder");
//Iterate the file from directory
foreach (FileInfo file in dir.GetFiles(String.Format("*_{0}.txt", User.Identity.Name)))
{
//Open and read the file
TextReader text = StreamReader(file.FullName);
Console.WriteLine(text.ReadLine());
}