My Itunes has an unauthorized name on it The name "Deepali Goal" has appeared on my Itunes. It is in a tab shaped like a house. When I click on this I have an option for My Library or Deepali Goal's Library. What does this mean??
Your Apple account may be compromised and some (not so smart) idiot logged into it and enabled Home Sharing, that causes his media library to appear on your side and most likely yours also appears on his side.

Change your Apple account's password and consider enabling two-factor authentication on it, but most importantly try to understand how he got the password; was it a really bad password and he got lucky via brute force, or something more serious like a compromise of your computer or e-mail account ?