How to change my iphone 4s home computer?

I've had my Iphone 4 for a while now but I would like to change its 'home computer' which is basically the computer I can plug my phone into if I forget my password or whatever and will instantly unlock it, and over stuff… Because I shared a computer with my family but now have got a new laptop that iTunes works well on (not an apple product) I would like to have my own stuff on my own computer…
Oh, and how do I change the name of the phone?

You need to plug your phone into your new computer and it will ask you if you want to change the home (not the exact words, but I can't remember what it says) and you should say yes. Next, it will transfer the info from your iPhone onto your iTunes on your new computer so that it will have all of your music and apps. Renaming it? It should either ask you if you'd like to rename it or you SHOULD be abled to double click on the left side and type in your new name! The great thing is, everything will still be on your old computer, so if you ever have a problem, in the future, if you sync it and it end up doing something or deleting you apps or something crazy on accident, you can plug it into your old one, and it will have all of the stuff you left it with!
Hope this helped!