What was really begun was the profanation of the Name of Jehovah.  They began to call something by the Name of Jehovah.  The A. V. suggests "themselves", in the margin.  But the majority of the ancient Jewish commentators supply the Ellipsis by the words "their gods"; suggesting that they called the stars and idols their gods, and worshipped them.

The Targum of Onkelos explains it: 

"then in his days the sons of men desisted from praying in the Name of the Lord."

The Targum of Jonathan says: 

"That was the generation in whose days they began to err, and to make themselves idols, and surnamed their idols by the Name of the Word of the Lord."

Kimchi, Rashi, and other ancient Jewish commentators agree with this.  Rashi says:

"Then was there profanation in calling on the Name of the Lord."

Jerome says that this was the opinion of many Jews in his days. Maimonides, in his Commentary on the Mishna (a constituent part of the Talmud), A.D. 1168, in a long treatise on idolatry, gives the most probably account of the origin of idolatry in the days of Enos. The name Enos agrees with this, for his name means frail, weak, sickly, incurable.  The sons of men, as "Enosh", are so called for a similar reason (Job 7:17; 15:14.  Ps. 9:20; 103:15.  Dan. 2:43).  See Ap. 14.

If Jonathan, the grandson of Moses, became the first idolatrous priest in Israel (see notes on Judg. 18:30), what wonder that Enos, the grandson of Adam, introduced idolatry among mankind.

Moreover, what "ungodliness" did Enoch, "the seventh from Adam" have to prophesy about in Jude 14, 15, if purity of worship was begun in the days of Enos, instead of profanation in calling on the Name of the Lord? Surely this is sufficient evidence that this profanation of the Name of the Lord was the reason why Enoch was raised up to prophesy against it.