You are not able to rename the drive letter that contains the Windows operating system. This is because Windows files rely on the assigned drive letter staying the same, and your computer needs to know which hard drive it can load Windows from.
Master Boot Record and Partitioning Hard Drives
Whether a drive is labeled "C" has nothing to do with whether windows boots from that drive or not. When you computer boots, it load Windows from the files on whatever drive the Master Boot Record (MBR) tells it is a bootable partition. You may have copied over the C drive, which is a partition, but you have not changed the MBR, which is a segment of code outside of the partitions, commonly referred to as the partition table.
As you computer was setup, the C drive partition was created on the original hard drive. If you are not familiar with partitioning, it is essentially the process of creating a section on the physical hard drive that will serve as a "virtual" disk within windows. A single drive could be partitioned into many drives, such as a C drive, D drive and E drive; all at the same time. If you have multiple physical drives, as is currently the case, then you will have at least a C drive on your original disk, and an additional drive letter for the SSD (assuming you have them both connected at the same time).
The MBR keeps track of the partitions and which ones can be booted from. When the OS is installed on that C drive, it added a flag to the MBR which tells the bios that this partition is bootable. That way, when the bios goes looking for potential drives to boot to, it finds the C drive and starts loading windows.
Some of this information and a great deal more can be found in this about article, which nicely summarizes the MBR:
Wikipedia has a more indepth article on the topic: http://en.wikipedia.org/wiki/Master_boot_record
Moving Windows to a New Drive/Partition
In your case, you want the computer to start booting from you SSD. There are multiple ways to go about this. The easiest and least technically demanding is to reinstall windows onto your SSD. If you have not already, you can use the recovery disc creation program that came on your computer to create Factory Reset discs. Then, use these discs to install windows on your SSD. Finally, transfer any files you need from your old hard drive to the new one. I work for an IT firm and this something we do on a daily basis, when performing hard drive replacements.
There are some utilities that will allow you to edit the MBR and make drives bootable. I believe Parted Magic is one of these. However, I would not recommend this. You will have no end of trouble when you try to boot into windows on the new drive, even if it is a C partition, after being copied to a new HD with a different size/etc. I highly recommend you install windows using the factory reset disk.