The Quran

138

وَقالوا هٰذِهِ أَنعامٌ وَحَرثٌ حِجرٌ لا يَطعَمُها إِلّا مَن نَشاءُ بِزَعمِهِم وَأَنعامٌ حُرِّمَت ظُهورُها وَأَنعامٌ لا يَذكُرونَ اسمَ اللَّهِ عَلَيهَا افتِراءً عَلَيهِ ۚ سَيَجزيهِم بِما كانوا يَفتَرونَ

Muhammad Asad

And they say, "Such-and-such cattle and fruits of the field are sacred; none may eat thereof save those whom we will [to do so]" - so they [falsely] claim;¹ and [they declare that] it is forbidden to burden the backs of certain kinds of cattle; and there are cattle over which they do not pronounce God's name² - falsely attributing [the origin of these customs] to Him. [But] He will requite them for all their false imagery.

The pre-Islamic Arabs falsely claimed that these taboos were ordained by God, as is made clear in the last part of this verse. One of these supposed, arbitrary "ordinances" laid down that only the priests of the particular idol and some men belonging to the tribe could eat the flesh of such dedicated animals, while women were not allowed to do so (Zamakhshari).
I.e., while sacrificing them to their idols (see also 5:103 and the corresponding note). It would seem from this allusion that, as a rule, the pagan Arabs did pronounce the name of God - whom they regarded as the supreme deity - over the animals which they slaughtered; in the above-mentioned exceptional cases, however, they refrained from doing so in the belief that God Himself had forbidden it.