I think this question related not only to agile but to teamwork in general.
When we are working in a team and each member is working a user story to complete how to avoid creation of duplicate classes and conflict?
I mean if my user story require the creation of class A and also my team member need the same class and created the same (he may create it with slightly different name), how would we plan so that we move smoothly?
User Stories are for communication with your customer. They are in customer's language and don't contain technical details like classes. When you start an iteration you should break down the User Stories in tasks. Tasks are in developer's language and can cover multiple stories.
I agree with @hansmaad. Agile is about communication. As in, actually talking to people on a regular basis. A user story is a reminder to have a conversation.
If you're doing XP, are you pair programming? Are you rotating pairs?
If you're doing Scrum, are you holding a daily standup?
Are you writing unit tests? Do you have customer acceptance tests? Are you practicing continuous integration?
There's still a risk of developers duplicating functionality, but it's not as high.
