Is Google Play rebranded app being pushed to India? My Android Market is still Android Market. I am eager to update it manually, but I prefer official way when payment is involved.

In India, only app store is available.. no music, book and movie store. So, I have been guessing maybe it'll not be pushed to India. Is there any such policies?
The "Market" to "Play" renaming is just a re-branding of the store.  It won't change any of the underlying availability or features.  You will have to ask Google (good luck!) about if/when additional feature will be made available in India.  So there is nothing to be gained by "upgrading", other than satisfying the Google marketing department.

Here are some details from the Google Play FAQ:

Q: What types of content are available in my country?
* Paid Apps: Available in these countries
* Movies: Available in US, UK, Canada, and Japan
* eBooks: Available in US, UK, Canada, and Australia
* Music: Available in US