Kevin
Larry Walston's response is a good source of information.

As I sent in an E-mail message to you directly, the designation "Mounted" is incorrect. The "Third Kentucky Infantry, CSA," was only so-named and designated by the Confederate Government. The Confederate Government authorized for the regiment to be mounted on horses but did not authorize a name change. The Federal Government / War Department started this conffusion when the started organizing and transcribing the Confederate records and made the word "Mounted" as part of the official name. As true historians we need to follow the correct Confederate Government designation. According to the records the regiment could also be called the "Third Kentucky Cavalry, CSA," as it shows up on many POW documents.
Greg