For the next version of my iPhone app say 1.3 I want to change the product name and i am keeping bundle identifier same as old version. Is it cause any problem in AppStore?
No, as long as you keep the bundle ID the same, it's considered to be the same app.
Additionally, in the iTunes Connect portal, you can rename your app when you submit a new version of your app. (I did this with version 2 of Sefira, which I renamed to "Ultimate Omer 2".)
Just bear in mind that your iTunes "slug" (http://iTunes.com/apps/appname) remains with the first app name.
If you want to change the name of the app as it appears on the device, change the "Bundle Display Name" property in the info plist file.