Is there any way by which we can rename the blob container name in windows azure ?
Now, you can rename containers with Microsoft's "Microsoft Azure Storage Explorer" (after version 0.8.3). You can also rename azure tables and file shares with this tool. See the release notes here.
Note that this feature has the following disclaimer during usage.
Renaming works by copying to the new name, then deleting the source item. Renaming a blob container currently loses the container's properties and metadata, and may take a while if there are lots of blobs.
Therefore this is not an actual renaming behind the scenes and incurs read/write/transaction costs.