Computer sharing information, I need to change Please help

My husband purchase me a new Mac book computer and I gave him my old one. Every time he uses my old computer and save something, it shows up on my new computer. How do I separate ownership. It appears my information is still being used on the old computer. Should I change the iTunes information, or name? it appears we are sharing information and I want to separate the two computers, so that his information does not show up on my computer.