Hi spk. How long was he in a relationship with this girl for? It sounds to me like it was a longterm relationship in which case people often take a while to completely move on from that. It's not that he wants her back and doesn't want you, it's more to do with just getting used to accommodating somebody, and then suddenly they're not in your life anymore. Ignore the fact that he called you by her name. That's happened to the best of us and you have to be big and mature and accept it as a simple mistake.
Jealousy is a healthy reaction. I would be concerned if my partner wasn't at least a little bit jealous about me, as otherwise I'd think he didn't care! But when it starts to consume you then you have to realise that you have a jealousy issue, and that this is YOUR issue alone. It's not fair on any partner to have to contend with another person's irrational problems. For starters, why don't you try not letting him know how jealous you are, i.e. not putting your problems onto him. After a while you'll find that you'll deal with it better on your own anyway.
With regard to these items that remind you of his ex, if he has forgotten about them then pick them up and pack them away in a drawer somewhere. DO NOT BIN THEM!! No matter how tempting it is!!
At the end of the day, spk, you have to realise that he's with you and not his ex. That's really all you need to know.