The year was 1529, the event was the Second Diet of Speyer, and the particular matter that brought about labeling of Evangelicals as 'Protestants' was their objecting to undemocratic religious prejudice regarding the reaffirmation of the Edict of Worms.
They did not give themselves that name but the label stuck, yet became much misunderstood by those unacquainted with the circumstances as to what, precisely, the Evangelicals were protesting about:
The Edict of Worms was reaffirmed only for Catholic territories. Provisionally, and prior to reaffirmation of the Edict of Worms by the general council, Lutheranism was to be tolerated in those regions where it could not be suppressed without tumult. By then, most of northern Germany had become Lutheran, and in the south the cities of Strassburg, Augsburg, Ulm, and Nurnberg. Constance embraced the reform, severed connections with the Hapsburgs, and joined the Swiss. Basel came over to the reform in 1529, the year of the Second Diet of Speyer. Between June 25th to August 27th 1526, the Diet of Speyer deferred action on the Edict of Worms. Here I quote:
"In Lutheran lands, the principle of religious liberty for Catholics
must be observed, whereas in Catholic lands the same liberty would not
be extended to the Lutherans. Against this invidious arrangement the
Evangelicals protested, whence the origin of the name Protestants.
They contended that the majority of one diet could not rescind the
unanimous action of the previous assembly. They questioned whether
this was the intent of the emperor, and on that score they were
correct. They affirmed that they could not have two religions side by
side in their territories without menace to the public peace, and if
their plea was not heard, then 'they must protest and testify publicly
before God that they could consent to nothing contrary to his Word.'
Their stand has been variously misinterpreted. In the Protestant camp
the emphasis has been all too much on the first word, 'protest',
rather than on the second, 'testify'. Above all else, they were
confessing their faith... In this protest the Zwinglians and Lutherans
were joined." Here I Stand by Roland Bainton, pp 317-8 (Lion, 1988)
I have gone over and above the simple question in order to put a little flesh on the bare bones of the answer: "April 19th, 1529".