Sorry you did not get any answer on Google's Forums! Hopefully this helps...
What happens when you close your Adsense account?
The AdSense account you currently have will no longer generate you money when you switch to a new account. I suggest getting the information that you currently have off of your current AdSense account (if you can still retrieve this information) by taking screen shots of information and exporting the information that you currently have throughout your AdSense account. This way when you create a new account you will be prepared to set it up just like the old AdSense account. The account you are using now will need be closed and a new account will need to be created because of the Payee Name situation. You will basically have to start over with your AdSense account but make sure you get all of the information from your current AdSense account that you need to setup a new account.
If I apply again, then what will be the process to re-gain my account? I mean should I have to apply for a website again, then Adsense team will review and approve that?
Yes, they will review it and either accept it or reject it. Unless you have done something that is against Google's policies you should have no problem with this. I would contact customer support and get their attention. Get everyone you can "in the know" and has an understanding of your situation. This way, if it is possible to migrate your current AdSense account settings to your new account you will be in good shape.
Is there any chance to disapprove my account?
I do not think so, unless you were directly violating their Terms and Conditions that you agreed to.
What about current check? I have two check in my hand. So, is Google will send those check again to me with my new payee name?
Number one, keep those checks and wait until you hear word from Google by telling them you have two checks that you need resent under your new Payee name. Get a hold of a Google Representative he or she should be able to work something out with you on the checks; so long as you have not tried to cash them. You will need to contact the AdSense billing department and explain your situation. You can also contact them at the AdSense Contact button on this page.
Google will more than likely restore your old account and have you use a different log-in with your name as the payee. If you have not violated any of the Terms of Service Google will be happy to assist you, in most cases, in my experience -- the downside is that it may take a while for them to get to you.