You can always go into Disk Management and set this up. But there cannot and won't be two Drives with the (C: ) letter, it will change by exemple to (F: ) or (E: ) etc. I installed my SSD today and copied my old HDD to my new SSD, and it automatically changed it once i switched the boot drive on the BIOS, you should just make sure to look into that, though. Goodluck !
And unless you want to backup, i'd make sure to Format the old Boot Drive ... Just making sure to avoid Conflict, otherwise, i do not know, i am not a complete knowledged person for that. But that is what i know, since i had the chance to do it.