Well, from a quick glance, you're trying to redirect the output of the ls command to a file called "Name" in your root directory. Only root (should) be able to modify files and directories there. You should have received an error message; when I try I get:
anthony@serenity:~$ ls /home/anthony >> /Name
bash: /Name: Permission denied
It's not a good idea to save files in /. Nothing's likely to happen, but then it looks like a mess like on other operating systems (ahem, Windows, why do you insist on saving Update Installtion, and other logs in C:\???).
Your other problem is if you are not replacing "/home/user" with your own directory, if in fact you typed into the terminal exactly what you described.
You must remember when following examples from books, the web, &c.; that certain words (usually boldface in books, or some other distinct type) are to be replaced with your own username, filename, etc.