When Chechen separatists proclaimed independence of the Chechen Republic, they used a name Chechen Republic of Ichkeria to refer independent Chechnya.
The Federal Russian government refuses to recognize the separatist Chechen government. There are no countries that officially recognize Chechen independence, probably in part to avoid jeopardizing their diplomatic relationships with Russia and to avoid encouraging separatists inside their own borders. In the past, the independence was recognized by Taliban (however, the Islamic State of Afghanistan has never recognized the Chechen independence too).