I contacted the Logitech and this is the reply:
Dear Prakash,
My name is Marissa R., I understand that you would like assistance with your G602 Wireless Gaming Mouse.
This is to inform you that it is normal that the serial number on your mouse is different on the box.
In line with warranty claim, Logitech based its products warranty from the date of purchase indicated on the receipt. We suggest for you to keep your product's receipt for future reference.
For future reference your case reference number is XXXXXXXXXX. This will allow us to quickly find the contact history when you need additional help. If we do not receive a reply, your support request will eventually be closed and set to "solved". A survey will be sent to you to gather your feedback.
To contact us by phone or obtain additional information (FAQ's, Forum, Manuals, etc.) please visit Logitech Support - Downloads, Manuals, FAQs & More.
Best regards,
Logitech Customer Care Team