The ad duration is set by you as the admin in the form of ad packs or your ad expiration settings in the ClassiPress admin, so no, the customer can't set this during the ad posting process. They can however end an ad early from within their customer dashboard by pausing it.
The name that the customer registers with is their log in name, but they can access their customer profile once they're logged in and set a Nickname and change the display name in there.