When was the Thirty Years War received it's name?

Answer 1

His story:

    23 May 1618 – 15 May 1648 [30 years  from 1618 to 1648]

(29 years, 11 months, 3 weeks, and 1 day)  

The Catholic Eradication of Protestantism; in much of the Habsburg Monarchy   

Beginnings of the change from religious to dynastic wars; Dutch independence and Swedish power over the Baltic.

Answer 2

Right after it started. All wars get their names in the beginning.