What is the name of Celtic language?

There is no single "Celtic language". "Celtic" refers to a family of languages, much like the Indo-European language family.

Here are some of the major Celtic languages:

* Insular Celtic

* Goidelic: Irish, Scottish Gaelic, Manx

* Brythonic: Welsh, Breton, Cornish

* Continental Celtic (extinct)

* Gaulish

* Celtiberian

* Lepontic

* Galatian

So, it depends on which specific language you're referring to!