Drag and drop files onto string variables in inspector to get the file name?

I dont follow excatly what you are doing but here a couple things i found that might help. You cant manually drag and drop files into a text asset variable. its pry something unity should fix. but anyways, you can do it with code like this:

     var mydoc:TextAsset;  
         mydoc = AssetDatabase.LoadAssetAtPath("Assets/rules.txt", typeof(TextAsset)) as TextAsset;
     
     print(mydoc.text);

here is code to grab anyfile anywhere and rename it if you want:

 // some of this stuff doesn't work with builds for certain platforms.
 
 import System.IO;
 import System.Diagnostics;
 
 var txt:String;
 var thefile:bytes[];
 var anypath:String;
 anypath="C:/ToddsGames/Killer Robots in Outer Space/";
 
 if(!System.IO.Directory.Exists(anypath)){
 System.IO.Directory.CreateDirectory(anypath);}
 
 // will grab anyfile reguarldess of extention 
 thefile=File.ReadAllBytes(anypath+"/anyfile.txt");
 
 //you would delete the file if you wanted to rewrite in the same place
 //with a different name
 File.Delete(anypath+"/anyfile.txt");
 
 //stick it back in the folder or anywhere you want with your new name.
 
 File.WriteAllBytes(anypath+"/newnamefile.txt",thefile);
 
 // if your file is a text file you can read it like this:
 txt=System.Text.Encoding.UTF8.GetString(thefile);