When including files in PHP, it acts like the code exists within the file they are being included from. Imagine copy and pasting the code from within each of your included files directly into your index.php. That is how PHP works with includes.
So, in your example, since you've set a variable called $name in your front.inc file, and then included both front.inc and end.inc in your index.php, you will be able to echo the variable $name anywhere after the include of front.inc within your index.php. Again, PHP processes your index.php as if the code from the two files you are including are part of the file.
When you place an echo within an included file, to a variable that is not defined within itself, you're not going to get a result because it is treated separately then any other included file.
In other words, to do the behavior you're expecting, you will need to define it as a global.