Syncing iphone 4 itunes to iphone 5

I have an iphone 4 and yesterday got the iphone 5. On my computer the new iphone has its own itunes independent of my iphone 4's. My iphone 4 holds all my music but I don't know how to get it to my 5. My 5 does not have the name that was given to my 4, it has no name - just simple 'iphone'.

How do I get the 4 itunes to recognise my 5 as it's replacement and take it's name?