Well, technically, it's a Concealed Hangun License. But, many states use different terminologies. It really depends on what state you're in. Below is a list of varying license or permit names:
CHL/CHP - Concealed Handgun License/Permit
CDWL/CWP/CWL - Concealed (Defensive/Deadly) Weapon Permit/License
CCP/CCL - Concealed Carry Permit/License
LTC/LTCF - License To Carry (Firearms)
CCDW - Carry of Concealed Deadly Weapon license
CPL - Concealed Pistol License
Etc.
Edit: Here's an interesting graphic I saw on wikipedia showing the varying right-to-carry laws across the United States:
Unrestricted - means no permit is needed to carry a concealed handgun
Shall-Issue - means a permit is required to carry concealed, and the permit shall be issued if a person meets the requirements set forth in the state laws
May-Issue - means a permit is required to carry concealed, and the local authorities have the the discretion of issuing the permit even if the person meets all requirements set forth in the state laws
No-Issue - no private citizen may carry a concealed handgun.